Proving Cauchy Sequence with Triangle Inequality

[birdibabe]

Homework Statement

Let S_n be a sequence such that |S_n+1-S_n|< 2^-n for all n in the natural numbers

Homework Equations

The Attempt at a Solution

I understand what it means to be cauchy but I'm not sure how to prove this particular sequence is cauchy. Please help!

 

[Dick]

Use the triangle inequality. For m>n, |S_m-S_n|<=|S_m-S_(m-1)|+|S_(m-1)-S_(m-2)|+...+|S_(n+1)-S_n|.