[![enter image description here](https://i.stack.imgur.com/NllD4.png)](https://i.stack.imgur.com/NllD4.png)

I tried many things, including ratio test, root test, comparison test, cauchy criterion, rewriting w.r.t e^n and doing all these tests again, but no luck in any direction. Any hints?

It seems most likely that I missed out on rewriting this stuff to resemble something that can be compared.