Good example. You could have made it slightly simpler by taking
Let and .
Prove or provide a counter example that converges.
I was wondering wether this is a valid counter example:
Let .
Then
And .
Now using the integral test we find that this series converges if and only if
converges.
Now:
So that the series diverges.
Is this correct, and if so is there a more straight forward way to do this?
Thank you.