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.

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    $\begingroup$ own thoughts??? $\endgroup$ – tired Sep 20 '16 at 15:48
  • $\begingroup$ Actually, this is not a duplicate as one of the questions is "With which known series i have to compare". $\endgroup$ – Yves Daoust Sep 20 '16 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 '16 at 16:32
  • $\begingroup$ @Did: that's precisely the question I guess, for a comparison test. $\endgroup$ – Yves Daoust Sep 20 '16 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 '16 at 16:36

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

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  • $\begingroup$ yes i got the point... Thanks a lot.. $\endgroup$ – neelkanth Sep 20 '16 at 15:51
  • $\begingroup$ you are welcome $\endgroup$ – E.H.E Sep 20 '16 at 15:51

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