Hi everyone,

I have struggled with this question for far too long and I am hopeful someone can help.

Let {x_{n}} be a sequence in R. Let 0<r<1 and suppose |x_{n+1}-x_{n|}<r^{n}for all n in N. I need to show {x_{n}} converges.

I know this can be done by showing {x_{n}} is a Cauchy sequence. I think I am on the right track for the first few steps. However, I quickly get lost. Please help.