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Possible Duplicate:
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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    similar question http://math.stackexchange.com/questions/50919/calculate-the-sum-of-the-infinite-series-sum-n-0-infty-fracn4n2011-10-04
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    In the same vein as the two questions cited above:$$\sum_{n=1}^\infty n x^n=\frac{x}{(1-x)^2}$$2011-10-04
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    In above links the upper limit is infinity.But here is n.2011-10-04
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    And the index of summation is $i$. This is somewhat confusing...2011-10-04

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