Value f a=?

enter image source here

1 Answer
Feb 26, 2018

a=7a=7

Explanation:

S_n = sum_(k=1)^n (n+1)/(a n^2+(n(n+1))/2)(k/(n+1))^aSn=nk=1n+1an2+n(n+1)2(kn+1)a or

S_n = (2(n+1))/(2an+n+1)sum_(k=1)^n (k/(n+1))^a1/nSn=2(n+1)2an+n+1nk=1(kn+1)a1n or

S_n = 2/(2an/(n+1)+1)sum_(k=1)^n (k/(n+1))^a1/nSn=22ann+1+1nk=1(kn+1)a1n 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