Question

What are the cosine Fourier series and sine Fourier series? And using that answer to compute the series given.

0 < x < 2. f(x) = 1 Use your answer to compute the series: ю -1)" 2n +1 n=1

Answer 1

] OLUL 2. we howe f= al finet founier consider even extension of fas as as to find Co-sine tranformation as followe. fw= V - 2 222 2 . lida. tx 4 =2. 2 vast] tes dos tido. 2 for ers max da con las hingga ), ana -2 0 bn=o So the founien eosine Series of fw is only constant function. defined of considen odd extension of fo by Now fe) = - -2 LLO o Ln22. 17 - da * ! '70 na tu fil dhe t!' - ₂* Y220 Sonce fas odd funtion anzo bn = $ 5*4@g'sin mna dai

2 =) bn=l 1 1. sin not da. 3 2 no = 2 NAT los naa noms do (i- cos no ) [lt (1)n-1 ']. 2 Hue ban-i 4 banco ON-1) in few) ban-i Sina (2n-1) na 2 n=1 8W 4 Sin (n-1) ra S 2n-1) LT 2 nal 2=) eve we get, peutting fwa 4 Sin @n-1) a n-1) a 2 n! (-1)^-! - 11 n=1 (2n-1) M8 G-1m-1 (2n-1) M/u le (~n ho = > mai (2n+1) Z (-in (2n+1) 1/4 - 1