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.
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1$\begingroup$ own thoughts??? $\endgroup$– tiredCommented Sep 20, 2016 at 15:48
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$\begingroup$ Actually, this is not a duplicate as one of the questions is "With which known series i have to compare". $\endgroup$– user65203Commented Sep 20, 2016 at 16:09
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$\begingroup$ @YvesDaoust Right, rather "not a real question" since we do not know what "known series" mean to the OP. $\endgroup$– DidCommented Sep 20, 2016 at 16:32
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$\begingroup$ @Did: that's precisely the question I guess, for a comparison test. $\endgroup$– user65203Commented Sep 20, 2016 at 16:35
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$\begingroup$ @YvesDaoust Yes, but the OP is supposed to know their own curriculum and the corresponding list of "known series" while we are not. $\endgroup$– DidCommented Sep 20, 2016 at 16:36
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1 Answer
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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
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$\begingroup$ yes i got the point... Thanks a lot.. $\endgroup$ Commented Sep 20, 2016 at 15:51
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