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

Question Number 33125 by prof Abdo imad last updated on 10/Apr/18

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

1) p r o v e t h a t λ u_{n + 2} - (1 + λ^{2}) u_{n + 1} + λ u_{n} = 0

2) p t o v e t h a t Σ 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