I decided that this statement was true but I couldn't find a concrete way of justifying it.if $\displaystyle (a_n)$ is strictly contracting then $\displaystyle \sum_{n=1}^\infty |a_{n+1}-a_n|$ converges.

Is this statement true or false?

I tried using $\displaystyle |a_{n+1}-a_n| \leq L|a_n-a_{n-1}|$ but i'm not sure how that really helps.