# Calculus-Infinite Series Pre-exam problem

Let $\Sigma_{n=1}^{\infty} a_{n}$ be a converged series.
We also know $a_{n}>0$ for every n. Let $b>1$ be a real number.
Prove: The series $\Sigma_{n=1}^{\infty} ( b^{a_{n}} -1 )$ converges.