I am trying to prove the following limit in formal terms.

lim n -> inf (n x^n) = 0, where |x| < 1

I dont want to use the L'hopitals rule or any other method that involves differentiation. I am trying to use the following sequence definition.

x --> x0 =

(0 < e ==> there exists and N. such that for all n. n >= N ==>

abs (x n - x0) < e

but have got stuck in the middle.

Any hints regarding this would be appreciated.

Thanks,