# Math Help - Converging series

1. ## Converging series

Hello,
I'm looking for an example of a converging series $\sum a_n$ , that it's convergence can be shown using Cauchy's root test but can *not* be shown using the ratio test.
Thanks

2. This is fairly standard, from Hyslop.
$a_n=2^{ (-n-(-1)^n)}$

3. Thank you!