Determine the sum of the following series:
Sorry for poor latex, that is supposed to say infinity.
How might we turn this into an easier function to deal with?
The Attempt at a Solution
So far I've only proved convergence of the series. I'm not really sure where to begin. Any help is appreciated. I've ran it through maple and come out with the sum equaling -ln(2).
I thought of trying to work backwards to see if this series was some sort of taylor expansion but I failed at that. I just don't see any elementary techniques. Obviously maple spotted something I haven't lol.