Let-consider-an-integer-serie-a-n-x-n-given-by-a-n-H-n-k-1-n-1-k-1-Find-out-the-largest-domain-D-of-convergence-of-that-integer-serie-2-x-D-explicit-the-sum-S-x-of-the-a-n-x-n

Question Number 66814 by ~ À ® @ 237 ~ last updated on 20/Aug/19

L e t c o n s i d e r a n i n t e g e r s e r i e {a_{n} x^{n}} g i v e n b y a_{n} = H_{n} = \underset{k = 1}{\sum^{n}} \frac{1}{k}

1) F i n d o u t t h e l a r g e s t d o m a i n D o f c o n v e r g e n c e o f t h a t i n t e g e r s e r i e

2) \forall x \in D, e x p l i c i t t h e s u m S (x) o f t h e {a_{n} x^{n}}

3) C a l c u l a t e \int_{- 1}^{1} S (1 - x) S (x) d x .