Question

What does the series converge to,

Summation from n=0 to infinity: ((k-1)/k)^n
where k is a real number greater than 1.

Answer 1

it converges to k

Answer 2

I just do not understand how this correlates to a geometric series. If I want to get epslim within .00001 say how do I show this?

Answer 3

let (k-1)/k= x

Answer 4

x=1-1/k since k>1 0<x<1