Question

(b) Determine for which values of x the following series converges and find the limit for all the values of x where the series converges: (-1)" sin(ne) n n=1 Does this series converge uniformly on R? (c) Find the value of M8 1 n4 n=1

Answer 1

وارات Siant - fm) n=1 Solu eina De Moivar's ofermula = COS (ng)+ i sin(na) about 2-1 Taylor Expomtion for the goosheipeal bronch at legorithm Logcit2)= - Film - Log (itein) = ² (Du eine > Im C-log Citeity) = (-1)". Giang Log Cite") = In latellti Ang Citely) - Arg Citein) = 2 fija Sinme -> - tatcmx) -) "Sinfre) >> - trinces) cos()) "Show) 2cos794) = -tami (tem(ns)) = Da Singh). It cost ME. Vi = ED"Sin (m) 27 f(x) = 1 o=Ang Citeit) is periode of posied: -37 CYS- -ALALT Tcra 35 They het 2 fish Shor is Convegent to fo) a 04 Foresier Series of few= ao i cances mathsin na Passeval Identity: a=ts franche an = Safe Cosmida .bn=/a Sofas Shaudhr het fra)=x2 cs anned with CamScanner on x T)

9. = kas arde E folis on Even fronction) an= Cosny 2Y Sinna 2 COSny Soffo) cosmuch = Secesnici = facesnicy mula2 formats pzz.com Snimas ma [visine + 24 COSMA - 2 Shan = [0+ en A (-3? _o Sinny n3 2 Coacto Eigh bn = y ffoad Sinnracha 20, frou Sihom is an odd fretien oran). >> 2**(4-9) = 16 km bent. A = 16 2 year Ź you 45 P.I a4 9 = 247%. On = 4/22 (1)", bn=0 kas prach aon du glazbit) 45033d (3) () 03) 90 n= Lot T4 90 nt 16 it MI 3 h = 1 h 2 hand >>%69) *** ? (1-0) = 2 ** 2 h - %**%* t = 16 h AI => sate's ) = 16 164 nant Scanned with CamScanner