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How to find the sum of this infinite series
How can I calculate result of $\sum\limits_{i=1}^n\cfrac{n}{2^n}$ ?
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3similar question http://math.stackexchange.com/questions/50919/calculate-the-sum-of-the-infinite-series-sum-n-0-infty-fracn4n – Andrew Oct 04 '11 at 17:51
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2In the same vein as the two questions cited above:$$\sum_{n=1}^\infty n x^n=\frac{x}{(1-x)^2}$$ – robjohn Oct 04 '11 at 18:06
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2In above links the upper limit is infinity.But here is n. – user16948 Oct 04 '11 at 18:19
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And the index of summation is $i$. This is somewhat confusing... – Oct 04 '11 at 19:03