Sum of the series $\sum_{1}^{\infty}\frac{n}{2^{n}}$ is





With which known series I have to compare the given series? Please help. Thanks.

  • 1
    $\begingroup$ own thoughts??? $\endgroup$
    – tired
    Sep 20, 2016 at 15:48
  • $\begingroup$ Actually, this is not a duplicate as one of the questions is "With which known series i have to compare". $\endgroup$
    – user65203
    Sep 20, 2016 at 16:09
  • $\begingroup$ @YvesDaoust Right, rather "not a real question" since we do not know what "known series" mean to the OP. $\endgroup$
    – Did
    Sep 20, 2016 at 16:32
  • $\begingroup$ @Did: that's precisely the question I guess, for a comparison test. $\endgroup$
    – user65203
    Sep 20, 2016 at 16:35
  • $\begingroup$ @YvesDaoust Yes, but the OP is supposed to know their own curriculum and the corresponding list of "known series" while we are not. $\endgroup$
    – Did
    Sep 20, 2016 at 16:36

1 Answer 1


Hint: $${\frac {x}{(1-x)^{2}}}=\sum _{n=1}^{\infty }nx^{n}\quad {\text{ for }}|x|<1\!$$ let $x=\frac{1}{2}$ to get what you want

  • $\begingroup$ yes i got the point... Thanks a lot.. $\endgroup$
    – neelkanth
    Sep 20, 2016 at 15:51
  • $\begingroup$ you are welcome $\endgroup$
    – E.H.E
    Sep 20, 2016 at 15:51

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