Question

Value f a=?

Answer 1

`a=7`

Explanation:

`S_n = sum_(k=1)^n (n+1)/(a n^2+(n(n+1))/2)(k/(n+1))^a` or

`S_n = (2(n+1))/(2an+n+1)sum_(k=1)^n (k/(n+1))^a1/n` or

`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`