If coverges?

Question

Coverges or diverges? If coverges find limit

(n with e is subscript)
en=n^2/2^n-1

Answer 1

By l'Hopital's rule lim f(x)/g(x) = lim f '(x)/g'(x) as x->a
Here
lim(en+1) = lim[2n/2n2^(n-1)] = lim [1/2^(n-1)] = 0 as n-> inf
Thus it converges to
lim(en) = -1 as n-> inf