Simple Manipultion - what am I missing?

[meb09JW]

Hi,

I'm not sure how to go from the top-right to the bottom left.

It seems like they have differentiated the top and bottom separately... but I think there is some e identity I have forgotten?

thanks!

 

[Karamata]

It looks like that for k=0 they use l'hopital's rule, because when k=0 you have 0/0 (but maybe this is not the limit). I don't know what is k,N,j, etc.

 

[vela]

Looks kind of sketchy to me. When k=0, they're dividing by zero, so you can't really say the sum is equal to that quotient. It's better if you go back and look at the original series for the k=0 case.