let give u_n = ∫_0 ^π ((cos(nx)dx)/(1−2λcosx +λ^2 )) 1) prove that λ u_(n+2) −(1+λ^2 )u_(n+1) +λ u_n =0 2) ptove that Σ u


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

$l e t g i v e u_{n} = \int_{0}^{π} \frac{c o s (n x) d x}{1 - 2 λ c o s x + λ^{2}}$ $1) p r o v e t h a t λ u_{n + 2} - (1 + λ^{2}) u_{n + 1} + λ u_{n} = 0$ $2) p t o v e t h a t Σ u_{n} i s c o n v e r g e n t a n d f i n d i t s s u m$
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