Question

η2 -1 Find the sum of the series Σ1 n=1 (m2 +1)2

Answer 1

0 0 soolion. The sum of the series 2, 도 n던 제 12 IN n-1 nel (제2 을 1711 (7 nz) 2. (1)2 ) n21 2, n21 제 (1024] Izu 도 Q. 2 희 00 T 도 20 n에 1+1 hzo 1 nel (n2tile (ร์ - nza Carrie ( 1 + ( Z n20 IzU W nd | r20 + Taeye) (-1) t 2 Z inza series n2t n2o al isa known n러 h20 with 2 4.Cot(xs) 나 22 at is 2 nzo na aben aoel z 찌ooth lax.)ㅓㅗ CL A c1. Therefoche. 2, 에 Z 도 nal ncon21 (n22 1 M * Cothra) d T ㅓ 2. ( 쌓 (MA에 TTF 2 nal (A) 8 2 I_ acothla) + t 22 20-21 nell antrai ㅗ 2.m) 2(n-12 Ynik the Scicl

→ 14 excothG) 2 을 ㅗ 2 + C nel 2ln+i)2 2ln-i12 n2 2. ? 도 nel 2n42 - Li shift the the series series byt 1) RN - 글 rol) ( tory) + 2. ty ) It Toth(t) e ( 8 Corentiti? C 2 n21 antzi 21 T 도 tone + 2 21n12 - 'L LE Intri + ( 2n-2i nal Pol1 M the constant out of the series t ㅏ ~ 을 다 2 ㅓ 2M-12 12v antri 개 h2l 글 xer) . trail) 는) Ethia) (1) A cothla) ㅓ 커 2. . '2 을 h2l 2n-i)2 ㅓE nel br. known as seties 을 n20(ntHi2 IT IN neun

It is nzo nzo, tozlti Ž intuko)-no zs (no, do) ,n? with Therefore, -1/2 + ( 2 o entitije A cob kr LA) + 2 -- Ž nal la + nal 21n-il2 anthi 2 natri 2-4+15(2, Hilt Toth(*), & + 7 E nelzin-il2 2 لح E nal antzi n-zi) thiff the seves by c-1) - 1 / 1 --- po T [(1,147) Kita (*) -(1, Zin-in) but < (2, 441) 4 x cathia) ale netwol-in) El hot antzi 2n-zi - 1 ㅓ 2 + anani pull the constent out of the series 25+ (12,18). Recolher a la momenti2) + M8 ri À 7 nal antzi 2n+2i

12,1ti) acoth(a) 을 + ha (102 ㅓ 2 21 을 l +1 nal antzi 2n-U Ma h, known series C n20 (+1.02 it is, (707일 2 2 h2o (70,이, no z on o22) co z 1. 1 ㅏ른 ㅏ 2. Therefore, Zo ide-idea 212,143) + acother) ret) +1612, 1-)) all, Hiltothlx) ㅗ 2 2 2. 2 2 、 Z n21 2n12 2n-2) ( ㅏ른 ( 2 4) [22, 1-1)+ twth(x) t 2 ㅓ 2 +)) nal 2n12) . ah~ 20 -> - 글 + roth() + / Cr, Iri) tChi-i) . 2 2. * (1 - ipoli) tier)

simphly! L t A oth (A) = [h, Hila b. 14°/-2) C tipolli) 4 f(t, '- ) โL 2 0:56 3 6 D ๆ 44 we got, n -| 8N ๐ : 54 3 26 9 7 6 2 hz | (n1 1 ) -