SchoolTutoring Submission Error - Please provide a valid contact phone number.
Close

Not a member yet? Register now and get started.

lock and key

Sign in to your account.

Account Login

Forgot your password?

Finite and Infinite Mathematical Series

18 Apr Posted by in Algebra, Pre-Calculus | 511 comments

Overview:  What Is A Mathematical Series?

A mathematical series is the sum of the elements of a mathematical sequence.  If the series is finite, the sum will be a finite number.  For example, in the finite sequence {1, 2, 3, 4, 5}, the series is the sum of all the terms: 1 + 2 +3 +4 + 5 = 15.

Partial Sums and Sigma

Partial sums can be used, if the series is very long.  The final sum in the above example is easy to find, but it can also be approached by finding partial sums, such as the third partial sum in the series, S3, which is the sum of all the values of the first three numbers in the sequence, 1 +2 +3 or 6.  In formula terms, directions to find the sum are given by a Greek letter, sigma or ∑.

Infinite Mathematical Series

What is the mathematical sequence is infinite?  Finding the sum isn’t as easy as in a finite series, and the directions to find partial sums are very important.   For example, in the  series {2 + 4 +6 +… + 2n …} , the sum of the first term , S1=2, the second partial sum, S2, is 2 +4, or 6, and the third partial sum, S3, is 2 +4 +6 = 12.  The series will go on infinitely, because for every 2n, the nth term can always be one number larger.

Are All Mathematical Series Infinite?

The sum of many mathematical sequences is an infinitely large number, because n is infinitely large.  However, some mathematical sequences are infinite, but n becomes infinitely small, and the sum approaches a limit,  For example, suppose the mathematical sequence starts with a square with area 1, and then divide the square into halves.  The first rectangle will have an area 1/2 the size of the original square, the second rectangle will have an area 1/4 the size, the third will have an area 1/8, the fourth will have the area 1/16, and so on.  The pattern can be expressed as (1/2)1, (1/2)2, (1/2)3…(1/2)n…  If it is written as a series , then 1/2 +1/4 +1/8 +1/16 +… = 1, because the original square has area 1 and it was just divided into n rectangles.  The infinite series has a finite limit.

Real-World Applications Of Mathematical Series

Mathematical series have a number of useful applications.  For example, determining how much money will be earned with a recurring investment is an application of mathematical series used in banking.  There are a number of mathematical series that are used in radio and electronics, as well as in physics and computer science.

Interested in math tutoring services? Learn more about how we are assisting thousands of students each academic year.

SchoolTutoring Academyis the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Helena, MT visit: Tutoring in Helena, MT

  1. hefalimp cardijon07-28-14
  2. water damage restoration houston07-31-14
  3. cialis vente en ligne08-02-14
  4. achat cialis bon prix08-04-14
  5. online slots08-05-14
  6. chicken coop ideas08-05-14
  7. check this out,08-06-14
  8. video08-06-14
  9. cialis commercial08-06-14
  10. apple products08-07-14
  11. how to last longer during doggy08-07-14
  12. macarons bestellen08-09-14
  13. premature ejaculation tricks08-09-14
  14. cialis apcalis avis08-14-14
  15. palestinian goat sex08-14-14
  16. URL08-14-14
  17. how long is a good time to last in bed08-15-14
  18. buy pinterest likes08-16-14
  19. viagra08-17-14
  20. buy youtube likes08-17-14
  21. arganolie discount08-17-14
  22. cialis super active france08-17-14
  23. xlovecam hack tool 201308-18-14
  24. cheap viagra08-18-14
  25. beds online08-19-14
  26. Link08-19-14
  27. Sophia hills08-19-14
  28. Begum Law Group Alex Begum08-19-14
  29. click to08-19-14
  30. Pension08-19-14
  31. sick of law suits08-19-14
  32. Orlando vacation rentals near disney08-20-14
  33. seo training08-20-14
  34. Slendera08-20-14
  35. Bitcoin casino08-20-14
  36. Driving School Torquay08-20-14
  37. Bitcoin casino08-20-14
  38. escort in Sydney08-20-14
  39. Viagra08-20-14
  40. ροζ τηλέφωνα08-20-14
  41. attorneys08-20-14
  42. cupboards08-21-14
  43. kitchen cupboards08-21-14
  44. cupboards08-21-14
  45. Kids & Teens08-21-14
  46. Charles Floate08-21-14
  47. Flight Tickets08-22-14
  48. Richard McArthur Real Estate08-22-14
  49. DIRTY ARMY08-22-14
  50. Richard McArthur Reid Real Estate08-22-14
  51. Richard McArthur Belfair08-22-14
  52. ford raptor front bumper08-22-14
  53. Penis enlargement08-23-14
  54. cult education08-23-14
  55. raleigh wedding films08-23-14
  56. cult education08-23-14
  57. tadalafil in farmacia08-23-14
  58. sex08-24-14
  59. buy facebook likes08-24-14
  60. www.outlook.com08-24-14
  61. aqui08-24-14
  62. cheap ebikes08-25-14
  63. estrazioni lotto08-25-14
  64. edward maldonado08-25-14
  65. acheter cialis par paypal08-25-14
  66. Madden 15 glitches08-25-14
  67. insane value08-25-14
  68. dbz nappa vegeta raditz in one box toys08-25-14
  69. 1-800-411-pain08-25-14
  70. بفركس احتيال08-26-14
  71. emily blunt08-26-14
  72. emily bear08-26-14
  73. best online betting sites08-26-14
  74. Carey Martell08-26-14
  75. sex online08-26-14
  76. ford raptor bumper08-26-14
  77. metatron08-26-14
  78. Empower Network videos08-26-14
  79. Drywall Finishing08-26-14
  80. Knockdown Texture08-26-14
  81. Our Webpage08-26-14
  82. Illinois Process Serving08-27-14
  83. Albuquerque Appliance Repair08-27-14
  84. Loans08-27-14
  85. meal replacement shakes reviews08-27-14
  86. techni diag08-27-14
  87. Mclean dryer vent cleaning08-27-14
  88. vehicle locksmith08-27-14
  89. best google08-27-14
  90. wordpress plugin development08-27-14
  91. how to write a novel in 30 days or less08-27-14
  92. kvar08-27-14
  93. The New RemarkaMobile Program From Andrew Cass08-27-14
  94. werbung08-27-14
  95. network08-27-14
  96. Best online auction sites08-27-14
  97. FHA 203K08-27-14
  98. traffic lawyer los angeles08-27-14
  99. trustworthy people08-27-14
  100. renta de autos en cancun08-27-14
  101. rosary beads08-27-14
  102. SM in CSE08-27-14
  103. neolife omega-308-28-14
  104. irvine auto repair08-28-14
  105. Bee Wild Pest Control08-28-14
  106. renta de autos en cancun08-28-14
  107. frau befriedigen08-28-14
  108. http://www.law.fsu.edu/library/flsupct/91325/op-91325.pdf08-28-14
  109. Criminal Lawyer08-28-14
  110. physics chemistry biology tutor08-28-14
  111. Porno Filmes08-28-14
  112. used cars in chicago08-28-14
  113. legal highs uk08-28-14
  114. oaklawn mazda08-28-14
  115. Jual Add Follower08-28-14
  116. The easiest mortgage application you've ever seen!08-28-14
  117. dealer en chicago il08-28-14
  118. 13 of the hottest mortgage programs out there!08-28-14
  119. health insurance08-29-14
  120. scentsy deals08-29-14
  121. click here08-29-14
  122. eye doctor in tucson08-29-14
  123. Caralhos Grandes08-29-14
  124. games like epic inventor08-29-14
  125. Emma08-29-14
  126. advertise own property for sale08-29-14
  127. Afford a Home with these tips...08-29-14
  128. m8808-29-14
  129. 32 weken zwanger08-29-14
  130. Muita esporra08-29-14
  131. download app08-29-14
  132. AARON kocourek08-29-14
  133. apartamentos lisboa08-30-14
  134. online pharmacy08-30-14
  135. For Sale By Owner Boston MA08-30-14
  136. viagra08-30-14
  137. Lauralee Knowlton08-30-14
  138. best trading system08-30-14
  139. desktop computer reviews08-30-14
  140. machines sewing08-30-14
  141. Free android games08-30-14
  142. labor day greetings08-30-14
  143. moisturizing mask08-30-14
  144. servicios web nicaragua08-30-14
  145. 3d & abstract wallpapers08-30-14
  146. juicy couture tracksuits08-30-14
  147. gordas bailando menea tu chapa08-30-14
  148. maxxim tires details08-30-14
  149. http:getahome.info08-30-14
  150. pirater un compte facebook08-31-14
  151. Betboo08-31-14
  152. teen fantasy novels08-31-14
  153. payday loans08-31-14
  154. printing blocks08-31-14
  155. Squirrel Removal Katy08-31-14
  156. pirater un compte facebook08-31-14
  157. portable mini speakers08-31-14
  158. Coupons08-31-14
  159. cheap viagra08-31-14
  160. iphone608-31-14
  161. assfuck08-31-14
  162. optimizare online08-31-14
  163. trial key nod 3208-31-14
  164. Make Money Fast08-31-14
  165. Bodyguards08-31-14
  166. bets1008-31-14
  167. dog obedience training school09-01-14
  168. Bloomfield Hills09-01-14
  169. bee wild pest control09-01-14
  170. pest control houston review09-01-14
  171. appliance repair near Manhattan09-01-14
  172. Manhattan appliance repair09-01-14
  173. enjoy this very exciting web site09-01-14
  174. magnesium supplements09-01-14
  175. juicy couture on sale09-01-14
  176. Entertainment News09-01-14
  177. Uninterrupted Power Supply (UPS)09-01-14
  178. Cialis09-02-14
  179. viagra09-02-14
  180. openappmkt09-02-14
  181. data recovery mac09-02-14
  182. free cialis09-02-14
  183. Guitar Licks You’ll Love - “Stand By Me” on Guitar09-02-14
  184. canada business directory09-02-14
  185. diving cyprus09-02-14
  186. data recovery guru for mac09-02-14
  187. Free Download Register Software's09-02-14
  188. free mac data recovery software09-02-14
  189. Glendale appliance repair09-02-14
  190. House eviction09-02-14
  191. north county09-02-14
  192. viagra online09-03-14
  193. appliance repair Chandler09-03-14
  194. strange news09-03-14
  195. cheap viagra09-03-14
  196. oxycontin without prescription09-03-14
  197. hydrocodone online09-03-14
  198. buy tramadol09-03-14
  199. cheap viagra09-03-14
  200. Baltasar sanchez haz09-03-14
  201. click here09-03-14
  202. buy hydrocodone09-03-14
  203. sex09-03-14
  204. cheap viagra09-03-14
  205. adderall without prescription09-03-14
  206. free online slots machines09-03-14
  207. stop arguing09-03-14
  208. online slots free09-03-14
  209. #Counterparty unveils Multi-Signature Support09-03-14
  210. Denver DUI Lawyer09-03-14
  211. emotional intelligence training09-03-14
  212. sigue leyendo09-03-14
  213. rjswordprocessing.com09-03-14
  214. putas zorras09-03-14
  215. daily planner 201209-03-14
  216. carpet cleaners pretoria09-04-14
  217. Online Jobs09-04-14
  218. uméro fixe ou mobile09-04-14
  219. Blackhatgalaxy09-04-14
  220. complementos online09-04-14
  221. sinema izle09-04-14
  222. nlp practioner09-04-14
  223. BTCRumor - Rumors about bitcoin09-04-14
  224. voyage de noce maldives09-04-14
  225. their website09-04-14
  226. cash for gold09-04-14
  227. cars for sale in dubai09-04-14
  228. Glass Replacement in Tempe09-04-14
  229. search09-04-14
  230. Sports Cards09-04-14
  231. viagra09-04-14
  232. dalaman transfers09-04-14
  233. web designer perth09-04-14
  234. locksmith in Ann Arbor09-05-14
  235. dead sea mud mask09-05-14
  236. locksmiths Nottingham09-05-14
  237. International cherry blossom festival09-05-14
  238. online designers shop09-05-14
  239. click here for pay day loan review09-05-14
  240. Payday Loans09-05-14
  241. just click for review09-05-14
  242. ?????? ???? 3 ?????? ?????09-05-14
  243. mayweather vs maidana 209-05-14
  244. Exterminator Service Houston Texas09-05-14
  245. hbos09-05-14
  246. FanDuel Promo Code09-05-14
  247. Mr. Kuek09-05-14
  248. Pest Control Richmond Texas09-05-14
  249. epub gratis09-05-14
  250. reviews affordablepup09-05-14
  251. teen dating site09-06-14
  252. xlovecam generateur de code gratuit09-06-14
  253. emotional intelligence training09-06-14
  254. emotional intelligence training09-06-14
  255. free slot machines09-06-14
  256. New auto insurance09-06-14
  257. air conditioning sherman oaks09-06-14
  258. lace saree09-06-14
  259. cheap car insurance by zip code09-06-14
  260. online drugstore09-06-14
  261. glass09-06-14
  262. Cheap protein09-06-14
  263. cardiff apartments for rent09-06-14
  264. Wedding Photos09-06-14
  265. Winchester sunroom09-06-14
  266. opana tacoma detox center09-06-14
  267. Homeowners insurance quotes09-07-14
  268. kitchen store09-07-14
  269. arlington sunroom09-07-14
  270. springfield sunroom09-07-14
  271. auto quote09-07-14
  272. sunroom hagerstown09-07-14
  273. sunroom yorktown09-07-14
  274. germantown sunroom09-07-14
  275. Citibank Locations09-07-14
  276. columbia sunroom09-07-14
  277. nether hack09-07-14
  278. Free C#.NET Codes09-07-14
  279. sewa elf surabaya09-07-14
  280. xenical online09-07-14
  281. buy adipex09-07-14
  282. buy soma09-07-14
  283. centreville sunroom09-07-14
  284. buy ambien09-07-14
  285. buy ambien09-07-14
  286. code promo sarenza09-07-14
  287. buy vicodin09-07-14
  288. buy ativan09-07-14
  289. buy tramadol09-07-14
  290. cialis09-08-14
  291. Child sex abuse09-08-14
  292. kitchen fitters manchester09-08-14
  293. sex09-08-14
  294. Child abuse09-08-14
  295. tutorials09-08-14
  296. Sign-up today and get 40 FREE Coins!!!!09-08-14
  297. bdoutdoors09-08-14
  298. banana blue09-08-14
  299. Designer wallet09-08-14
  300. hearthstone arena guide09-08-14
  301. ubuntu09-08-14
  302. Weight loss for women09-08-14
  303. BedHead line at Bela Beauty Boutique09-08-14
  304. comment gagner de l'argent09-08-14
  305. family lawyer09-08-14
  306. network09-08-14
  307. How Much Mortgage Can I Get09-09-14
  308. free porn download09-09-14
  309. BUY VIAGRA09-09-14
  310. kundalini system09-09-14
  311. fb groups poster nikla09-09-14
  312. penis enlargement09-09-14
  313. Aspergers Quiz09-09-14
  314. web developer perth09-09-14
  315. Aspergers Quiz09-09-14
  316. islands holidays09-09-14
  317. Aspergers Quiz09-10-14
  318. iphone 5c case armorbox09-10-14
  319. Musician09-10-14
  320. musica09-10-14
  321. Cialis09-10-14
  322. tworzenie stron www lódz09-10-14
  323. seo services perth09-10-14
  324. investments09-10-14
  325. website designers perth09-10-14
  326. xylitol effects09-10-14
  327. zobacz oferte09-10-14
  328. relax musics09-11-14
  329. http://www.ath-m50.net/09-11-14
  330. cerrajero de murcia09-11-14
  331. loyal 9 reviews09-11-14
  332. west michigan wedding photography09-11-14
  333. snooki weight loss09-11-14
  334. Best Rated Best Rated appliance repair Chicago09-11-14
  335. Home Business Sims 209-11-14
  336. get products with master resale rights and giveaway rights09-11-14
  337. kitchen09-11-14
  338. angel lopez guia09-11-14
  339. Annapolis Maryland Movers09-11-14
  340. karadayi shqip09-11-14
  341. free netflix account09-11-14
  342. Viagra09-11-14
  343. cavaleiros do zodiaco09-11-14
  344. loan financing09-11-14
  345. buy google plus followers09-11-14
  346. Camilo Concha09-11-14
  347. pulseras de goma09-11-14
  348. sex landscaper09-12-14
  349. plymouth bjj09-12-14
  350. toshiba laptop akció09-12-14
  351. Wood Walking Sticks09-12-14
  352. Diabetes mallitus09-12-14
  353. how to network on facebook09-12-14
  354. salon semo09-12-14
  355. numéro de téléphone particulier09-12-14
  356. Coupons For Dog Foods09-12-14
  357. Caller ID Revenue09-12-14
  358. sehack09-12-14
  359. child custody lawyers09-12-14
  360. Gambling09-12-14
  361. ofertas peru09-12-14
  362. se hack09-13-14
  363. tension elevator cable physics09-13-14
  364. porady prawne zabrze09-13-14
  365. aromatherapy diffuser09-13-14
  366. polecane2409-13-14
  367. Chromebox09-13-14
  368. gold maps09-13-14
  369. share code snippets09-13-14
  370. thailand top up09-13-14
  371. Jennifer lawrence exposed in iCloud09-13-14
  372. iva09-13-14
  373. Mesa appliance repair09-13-14
  374. Awesome Self publishing blog09-13-14
  375. Mesa appliance repair09-13-14
  376. penis extender09-13-14
  377. Home Improvement Company09-13-14
  378. Washer repair09-13-14
  379. check these guys out09-13-14
  380. Explainer Videos09-13-14
  381. prêt sur salaire09-13-14
  382. minecraft online09-13-14
  383. StrategyDB.com custom TradeStation consulting09-13-14
  384. lawsuits xarelto09-14-14
  385. sex, porn09-14-14
  386. drugs09-14-14
  387. gay porn09-14-14
  388. זילכה שירלי09-14-14
  389. concrete coatings fort collins09-14-14
  390. New Zealand Street Wear09-14-14
  391. pages blanches09-14-14
  392. here for free09-14-14
  393. gay porn09-14-14
  394. vending machines melbourne09-14-14
  395. feelings09-14-14
  396. seo uzmanı09-14-14
  397. ecigarette review09-14-14
  398. buy instagram followers09-14-14
  399. Accident Attorney, Divorce Lawyers, Personal injury lawyers09-14-14
  400. garden shed plans09-14-14
  401. stopthestresstoday.com/contact09-14-14
  402. stopthestresstoday.com/about-me09-15-14
  403. cheap porn09-15-14
  404. celebrity nudes09-15-14
  405. Livejasmin codes09-15-14
  406. the plumbing cure09-15-14
  407. discount perfumes09-15-14
  408. sfi affiliate09-15-14
  409. watches for men on sale09-15-14
  410. coconut milk09-15-14
  411. Roaches for sale09-15-14
  412. cosmetica bio09-15-14
  413. LAX Car Service09-15-14
  414. LAX Car Service09-15-14
  415. zenith roofing fort worth09-15-14
  416. viking axis soap dish09-15-14
  417. newport beach09-15-14
  418. newport beach09-15-14
  419. Online ged classes09-15-14
  420. seo uk09-15-14
  421. Johnie Tilbury09-16-14
  422. Wigs Denver09-16-14
  423. online flashcards09-16-14
  424. agence web09-16-14
  425. forever living clean 9 results09-16-14
  426. filtros de agua09-16-14
  427. hr2409-16-14
  428. betboo09-16-14
  429. indicizzazione google09-16-14
  430. bahis sitesi09-16-14
  431. interactive 360 video09-16-14
  432. binary options review09-16-14
  433. drysol for hands09-16-14
  434. betboo09-16-14
  435. House Cleaning Sydney09-16-14
  436. vince stanzione09-16-14
  437. e-signature09-16-14
  438. web design dallas09-16-14
  439. mtv music09-16-14
  440. bahis sitesi09-16-14
  441. Post Education09-16-14
  442. betboo09-17-14
  443. süperbahis09-17-14
  444. aluminium gutters09-17-14
  445. betboo09-17-14
  446. chelsea ferguson gets tits out,09-17-14
  447. league coaching09-17-14
  448. Zebra Printer Repair09-17-14
  449. abacus09-17-14
  450. social businesses09-17-14
  451. atms for event09-17-14
  452. 5 min walk from Metro Place D'armes09-17-14
  453. guttering Surrey09-17-14
  454. Aspergers Quiz09-17-14
  455. Carter Hargrave09-17-14
  456. WP Profit Builder Review & Bonuses09-17-14
  457. locksmiths in Saline09-17-14
  458. alaska fishing09-17-14
  459. green laser module09-17-14
  460. Jogos de carros09-17-14
  461. ganool09-17-14
  462. cheap viagra09-18-14
  463. TRADEMARK LAW09-18-14
  464. alaska fishing09-18-14
  465. like it09-18-14
  466. Patriot Rooter09-18-14
  467. alaska fishing trips09-18-14
  468. frozen surprise eggs09-18-14
  469. sub zero service locator09-18-14
  470. courier services in hyderabad09-18-14
  471. industrial units to let london09-18-14
  472. best Wilmington photographer09-18-14
  473. additional reading09-18-14
  474. M8809-18-14
  475. flyinghomes09-18-14
  476. Decal09-18-14
  477. nagrobki warszawa09-18-14
  478. Toys & Games09-18-14
  479. esta web sobre la alcachofa de laon09-18-14
  480. biuro podatkowe szczecin09-18-14
  481. unfollowers09-18-14
  482. easy money09-18-14
  483. Best astrologer in india09-18-14
  484. fut 15 coins09-18-14
  485. search engine optimization pricing09-18-14
  486. Joe Pojman09-18-14
  487. Garage door repair09-18-14
  488. click here now09-18-14
  489. Ricker Construction - Snow Removal and Excavation Services in Harrisburg PA09-18-14
  490. printable oil change coupons09-19-14
  491. click site09-19-14
  492. www.canabista.com09-19-14
  493. larin chat09-19-14
  494. éjaculation précoce comment faire09-19-14
  495. éjaculation précoce comment faire09-19-14
  496. kangen water machine09-19-14
  497. Paul Mush09-19-14
  498. Gate repair09-19-14
  499. Julefrokost09-19-14
  500. télécharger des films gratuitement09-19-14
  501. casino09-19-14
  502. lampy09-19-14
  503. Corona CA09-19-14
  504. event space09-19-14
  505. Ocean Isle Wedding Photographer09-19-14
  506. Familienanwalt Enger09-19-14
  507. soigner éjaculation précoce09-19-14
  508. Formula T1009-20-14
  509. ripoff report09-20-14
  510. bob nokley09-20-14
  511. false09-20-14