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.