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How can sum the infinite series whose nth term is 1/n * ((x^n - 1)/(x + 1) ^n)
How can sum the infinite series whose nth term is
1/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 ExpertsSoumyajit Das IIT Kharagpur
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