Answer
Converges
Work Step by Step
We have: $a_k=\dfrac{1}{5^k-3^k}$ and $b_k=\dfrac{1}{5^k}$
Now, we need to apply the limit comparison test.
$L=\lim\limits_{k \to \infty}\dfrac{a_k}{b_k}\\=\lim\limits_{k \to \infty}\dfrac{\dfrac{1}{5^k-3^k}}{1/5^k}\\=\lim\limits_{k \to \infty}\dfrac{1}{1-(3/5)^k} \\ \dfrac{1}{1-0}\\=1$
Therefore, the series converges by the limit comparison test.
