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

$a.1$

$b.2$

$c.3$

$d.4$

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

Martin Sleziak
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neelkanth
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    own thoughts??? – tired Sep 20 '16 at 15:48
  • Actually, this is not a duplicate as one of the questions is "With which known series i have to compare". –  Sep 20 '16 at 16:09
  • @YvesDaoust Right, rather "not a real question" since we do not know what "known series" mean to the OP. – Did Sep 20 '16 at 16:32
  • @Did: that's precisely the question I guess, for a comparison test. –  Sep 20 '16 at 16:35
  • @YvesDaoust Yes, but the OP is supposed to know their own curriculum and the corresponding list of "known series" while we are not. – Did Sep 20 '16 at 16:36
  • See also http://math.stackexchange.com/questions/1330493/how-do-you-prove-sum-frac-n2n-2 or http://math.stackexchange.com/questions/337937/why-sum-k-1-infty-frack2k-2 – Martin Sleziak Oct 02 '16 at 03:44
  • https://math.stackexchange.com/questions/1788459/sum-of-the-series-sum-fracn2n/1788477#1788477 – Bijesh K.S Oct 02 '16 at 04:54

1 Answers1

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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

E.H.E
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