Find the sum of the series $\sum_{i = 0}^{n} \frac{i}{2^i}$.
I already have a solution of it in the book but it is long, so can anyone tell me a short solution for this?
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1Did you already try to look here at MSE? – Dietrich Burde Jan 10 '19 at 20:25
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thank you @DietrichBurde but is it a short solution ? – Intuition Jan 10 '19 at 20:27
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1Yes, it is really short, just geometric series and a bit in addition in Andre's answer. – Dietrich Burde Jan 10 '19 at 20:28
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1@hopefully Look at the last solution on that page, using differentiation. If you're familiar with calculus then that is a very short solution. – AlephNull Jan 10 '19 at 20:29
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1@hopefully "guess" the solution and then prove by induction (2 lines proof and you're done). – Yanko Jan 10 '19 at 20:31