# How do I expand/solve the following summation? [duplicate]

$\sum\limits_{i=1}^{n-1} i$.

I know the answer is $\frac{1}{2}(n-1)n$ but I don't quite understand it how to get there.

## marked as duplicate by Jack D'Aurizio, Newb, graydad, k170, apnortonMay 2 '15 at 17:12

• Sum up term by term the two previous lines, i.e. the $1$ with the $n-1$, the $2$ with the $n-2$ and so forth. The addition always yields $n$. Now, how many times are we summing up? $n-1$. – Demosthene May 2 '15 at 10:35