let A_p =Σ_(n=1) ^∞ n^p x^n with p integr . and x ∈]−1,1[ . 1) calculate A_1 ,A_2 and A_3 2) find a relation of recurrence betwen the A_n 3) calculate Σ_(n=1) ^∞ n^4 x^n and Σ


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Question Number 46849 by maxmathsup by imad last updated on 01/Nov/18

$l e t A_{p} = \sum_{n = 1}^{\infty} n^{p} x^{n} w i t h p i n t e g r . a n d x \in] - 1, 1 [.$ $1) c a l c u l a t e A_{1}, A_{2} a n d A_{3}$ $2) f i n d a r e l a t i o n o f r e c u r r e n c e b e t w e n t h e A_{n}$ $3) c a l c u l a t e \sum_{n = 1}^{\infty} n^{4} x^{n} a n d \sum_{n = 1}^{\infty} n^{5} x^{n} .$
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