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Value f a=?

1 Answer

Feb 26, 2018

$a = 7$ $a=7$

Explanation:

$S_{n} = n \sum k = 1 \frac{n + 1}{a n^{2} + \frac{n (n + 1)}{2}} {(\frac{k}{n + 1})}^{a}$ $S_n = sum_(k=1)^n (n+1)/(a n^2+(n(n+1))/2)(k/(n+1))^a$ or

$S_{n} = \frac{2 (n + 1)}{2 a n + n + 1} n \sum k = 1 {(\frac{k}{n + 1})}^{a} \frac{1}{n}$ $S_n = (2(n+1))/(2an+n+1)sum_(k=1)^n (k/(n+1))^a1/n$ or

$S_{n} = \frac{2}{2 a \frac{n}{n + 1} + 1} n \sum k = 1 {(\frac{k}{n + 1})}^{a} \frac{1}{n}$ $S_n = 2/(2an/(n+1)+1)sum_(k=1)^n (k/(n+1))^a1/n$ then

$lim_(n->oo)S_n =2/(2a+1) int_0^1xi^a d xi = 2/(2a+1)1/(a+1)$

Now $2/((2a+1)(a+1))=1/60$ and solving for $a$

$a = {-17/2, 7} rArr a = 7$

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