The given series is geometric with common ratio , which converges if (i.e. the interval of convergence). We have the well-known result
If you're not familiar with that result, it's easy to reproduce.
Let be the -th partial sum of the infinite series,
Multiply both sides by the ratio.
Subtract this from to eliminate all the powers of the ratio between 0 and .
Solve for .
Now as , the exponential term converges to 0 and we're left with