Hiya guys!

Could someone correct this for me please?Not sure if I went about it right at all!

Determine the sum of the series

What I did so far was:

The partial sum:

Rewritten as:

(I don't really know why I did this to be honest, I was mostly copying a similar sum from the book, so more than likely gone wrong with that line)

So...did I go completely wrong??Or where do I go from here to prove it's convergent and what is??

Thanks for your help guys!!

Jo