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08.02 - 8.2 INFINITE SERIES M 2(1 —(2" 2 1 S“(l—r...

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Unformatted text preview: 8.2 INFINITE SERIES M ._ 2(1 — (2%)") _. ' _ 2 _ 1' S“_ (l—r) _ l—Gj z} nleoo S“_ 1— 3 _ 3 S :—a(1__rn):l~—le)fl é um S = 1 :2 ' ’1 (l—r) 1— —§ n—aoo ” {iii 3 S'mmn;1_ni2 2} Sn2(%_%)+(%_%)+m+(ni1‘ni2): 15' m=fi—fi :‘ Sn=(1-%)+(%-%)+(%-1‘-3)+-~Hfi-m) "'(4111—3'Efi'li'r‘i')21'4nl+1z> nlipmoo Snanmoo (1—4nl+1) 1 23. convergent geometric series with sum $7 = fl = 2 + x/i 2 24. divergent geometric series with [r1 2 fl > 1 25. convergent geometric series with sum 27. 111351100 cos (mr) = “ii—{“00 (—1)’1 51E 0 => diverges 31. convergent geometric series with sum 2 — 2 : g9 — $§~ : 3 1__ ($3 9 9 9 33. difference of two geometric series with sum 1 1 2 — 1 1 1 = 3 — g = g — 3 — 3 . f __ . 35. ]“1333100 1530,, — 00 7k 0 => dlverges 00 00 41. Z30 (—1)“x’l 2 §(—x)“; a m 1,r m —x; converges to 1_1(_x) z 1}” for [xi < 1 n— n— __ -x—l. 3 _ 6 43.a—3,r— 2 ,convergestol_ x—i _3_x 2 for—1<"§—1<lor—1<x<3 ...
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