A more general criterion of convergence is that and converges...
A part of my course complex-analysis we deal with infinite products. And as a homework assignment I got the following exercise.
If for all , then prove that converges iff
I'm used to not so easy homework-assignments, so that's why I feel I'm missing something here.
My answer would be:
if we have since for all . Hence and thus we obtain
If we have
So am I missing something?
Now use the fact that the logarithm function and its inverse are continuous to argue that converges iff converges, as .