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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)


Grade:

1 Answers

Askiitians Expert Soumyajit IIT-Kharagpur
28 Points
11 years ago

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

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All the best Nehal Wani !!!

 


Regards,

Askiitians Experts
Soumyajit Das IIT Kharagpur

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