How can sum the infinite series whose nth term is1/n * ((x^n - 1)/(x + 1) ^n)

Dear  Nehal Wani,

Ans: Do you know the log seriess? These are

log(1+x)=x-x²/2+x³/3- ...............

log(1-x)=-(x+x²/2+x³/3+...............)

In your problem there are 2 log series those are

log(1-p)  &&  log(1-q)

where p=x/(x+1)  q=1/(x+1);

Hence the sum is=log(1-q) - log(1+q)

=log[1-x/(x+1)]-log[1-1/(x+1)]

=log[x/(x+1)]-log[1/(x+1)]

=logx

Please feel free to post as many doubts on our discussion forum as you can. If you find any question
Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We
are all IITians and here to help you in your IIT JEE preparation.

All the best Nehal Wani !!!

Regards,

Askiitians Experts
Soumyajit Das IIT Kharagpur