let r∈[0,1[ and θ ∈ R,x∈ R prove that 1) 1+ 2 Σ_(n=1) ^(+∞) r^n cosθ = ((1−r^2 )/(1−2r cosθ +r^2 )) 2)1 =(1/(2π)) ∫_0 ^(2π) (((1−r^2 ))/(1−2rcos(t−x) +r^2 ))dt


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Question Number 35605 by abdo mathsup 649 cc last updated on 21/May/18

$l e t r \in [0, 1 [a n d θ \in R, x \in R p r o v e t h a t$ $1) 1 + 2 \sum_{n = 1}^{+ \infty} r^{n} c o s θ = \frac{1 - r^{2}}{1 - 2 r c o s θ + r^{2}}$ $2) 1 = \frac{1}{2 π} \int_{0}^{2 π} \frac{(1 - r^{2})}{1 - 2 r c o s (t - x) + r^{2}} d t$
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