Sunday 25 August 2013

limits - Find the value of the series $sumlimits_{n=1}^ infty frac{n}{2^n}$

Find the value of the series $\sum\limits_{n=1}^ \infty \dfrac{n}{2^n}$



The series on expanding is coming as $\dfrac{1}{2}+\dfrac{2}{2^2}+..$



I tried using the form of $(1+x)^n=1+nx+\dfrac{n(n-1)}{2}x^2+..$ and then differentiating it but still it is not coming .What shall I do with this?

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