let-give-lt-1-and-u-n-0-pi-cos-nx-1-2-cosx-2-prove-that-n-0-u-n-is-convergent-and-find-its-sum-

Question Number 31747 by abdo imad last updated on 13/Mar/18

l e t g i v e ∣ λ ∣< 1 a n d u_{n} = \int_{0}^{π} \frac{c o s (n x)}{1 - 2 λ c o s x + λ^{2}}

p r o v e t h a t \sum_{n = 0}^{\infty} u_{n} i s c o n v e r g e n t a n d f i n d i t s s u m .

Commented by abdo imad last updated on 14/Mar/18

u_{n} = \int_{0}^{π} \frac{c o s (n x)}{1 - 2 λ c o s x + λ^{2}} d x .