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I am beginner and a novice for sums and math in general. I don't know the steps or techniques to understand how does the right hand side equals the left? Could someone clarify the techniques or steps taken? Or direct me to a resource that could?

$$\sum _{i=0}^{\lfloor \log_2 n \rfloor}\Bigl\lfloor \dfrac {n}{ 2^{i}} \Bigr\rfloor= 2n $$

enjoylife
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    $\sum\limits_{i=1}^{\lfloor \log_2 n \rfloor}\dfrac{n}{2^{i}}=2n-1$? This equation is wrong. For $n=1$, the left side is $0$ and the right side is $1$. For $n=2$, the left side is $1$ and the right side is $3$. For $n=3$, the left side is $1.5$ and the right side is $5$... – barak manos Apr 02 '14 at 19:46
  • If the sum started at $i=0$ rather than $i=1$, then it would be correct whenever $n$ is exactly a power of $2$. Perhaps that's what was intended? – Greg Martin Apr 02 '14 at 20:12
  • Yes, I edited it accordingly – enjoylife Apr 02 '14 at 23:50

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