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Question Number 47065 by maxmathsup by imad last updated on 04/Nov/18

l e t v_{n} (a) = \int_{\frac{1}{n}}^{n} (1 - \frac{a}{x^{2}}) a r c t a n (1 + \frac{a}{x}) d x w i t h a > 0

1) d e t e r m i n e a e x p l i c i t f o r m o f v_{n} (a)

2) s t u d y t h e c o n v e r g e n c e o f \sum_{n} v_{n} (a)

3) c a l c u l a t e v_{n} (1) a n d \sum_{n} v_{n} (1) .