In my study on some type of integrals I met the series below that I don't how to approach it.
Of course, one of the obvious questions is: does it have a closed form? Before answering that,
I need to learn how to tackle them, the proper tools to employ. Any help on this series is very welcome. The use of $\arcsin(x)$ series expansion wasn't fruitful.
$$\sum_{n=0}^{\infty} \arcsin\left(\frac{1}{e^n}\right)$$
that more generally can be considered as
$$\sum_{n=0}^{\infty} \arcsin\left(x^n\right)$$