Let consider an integer serie {a_n x^n } given by a_n = H_n =Σ_(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 } 3) Calculate ∫


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Question Number 66814 by ~ À ® @ 237 ~ last updated on 20/Aug/19
$Let consider an integer serie {a_n x^n } given by a_n = H_n =Σ_(k=1) ^n (1/k) 1) Find out the largest domain D of convergence of that integer serie 2) ∀ x∈D , explicit the sum S(x) of the {a_n x^n } 3) Calculate ∫_(−1) ^1 S(1−x)S(x) dx .$
$L e t c o n s i d e r a n i n t e g e r s e r i e {a_{n} x^{n}} g i v e n b y a_{n} = H_{n} = \underset{k = 1}{\sum^{n}} \frac{1}{k}$ $1) F i n d o u t t h e l a r g e s t d o m a i n D o f c o n v e r g e n c e o f t h a t i n t e g e r s e r i e$ $2) \forall x \in D, e x p l i c i t t h e s u m S (x) o f t h e {a_{n} x^{n}}$ $3) C a l c u l a t e \int_{- 1}^{1} S (1 - x) S (x) d x .$
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