Hi everyone,
I have struggled with this question for far too long and I am hopeful someone can help.
Let {xn} be a sequence in R. Let 0<r<1 and suppose |xn+1-xn|<rn for all n in N. I need to show {xn} converges.
I know this can be done by showing {xn} is a Cauchy sequence. I think I am on the right track for the first few steps. However, I quickly get lost. Please help.