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$T(1) = 2$

$T(n) = T(n-1) + n/2$

My guess is this would be equivalent to $T(n) = 2 + \sum\limits_{i=2}^n \frac{n}{2^{i-1}}$. However, I don't know how to advance from here.

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HINT Note that $$ \begin{split} T(n) &= T(n-1) + \frac{n}{2} \\ &= T(n-2) + \frac{n-1}{2} + \frac{n}{2} \\ &= \ldots \\ &= T(n-n) + \sum_{k=1}^n \frac{k}{2} \\ &= T(0) + \frac{1}{2} \sum_{k=1}^n k \end{split} $$

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    $\begingroup$ You seem to be operating under the impression that the OP's guess was correct. Have you checked that? $\endgroup$ – JMoravitz Aug 3 '16 at 4:08
  • $\begingroup$ @JMoravitz fixed, thank you $\endgroup$ – gt6989b Aug 3 '16 at 4:14

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