Ok you want to compute:
Note that
So:
It's a telescoping sum , thus shaking off we have:
Im trying to find a closed form for the nth partial sum of the series ln(1/2)+ln(2/3)+ln(3/4)+...+ln(k/(k+1))+....
My book only has a paragraph on this and i cant understand what they're doing, can someone please try explaing this to me a little better?
Thanks