Does the following series converge? If it does, determine the appropriate limit.
The only thing i noticed so far is the occurence od the telescopic series via a transformation:
The ratio test delivers the result $k/(k+3)$ which renders it unhelpful, so I have to try something else. Now I have been thinking about finding an explicit expression for the partial sums
however I neither know, how do so nor do I know whether it suffices to show, that the partial sums will converge for $N\to\infty$ to conclude that the whole series will have a limit.
I need help on how to determine the the explicit expression of the partial sums and would like to know some good suggestions on what to do else.