# Solving the following recurrence

$T(1) = 2$

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

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.

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