let-A-p-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-n-1-n-4-x-n-and-n-1-n-5

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} .