Hey there, I'll be delighted to get some help in this question:

Let $\displaystyle \Sigma_{n=1}^{\infty} a_{n} $ be a converged series.

We also know $\displaystyle a_{n}>0$ for every n. Let $\displaystyle b>1 $ be a real number.

Prove: The series $\displaystyle \Sigma_{n=1}^{\infty} ( b^{a_{n}} -1 ) $ converges.

Thanks in advance...