# Sum of finite series?

How do I go about calculating the sum of this finite series? Below is the series and the sum:

$$\sum_{i=0}^{n^2-1}i$$

I understand that you have to use the formula: $\sum_{i=1}^{n}i = \frac{n(n+1)}{2}$ and that the answer is: $\frac{n^4-n^2}{2}$. I just don't know the steps to get there. I'm being thrown off by the starting index of $i=0$.

• The first term contributes nothing to the overall sum... – user170231 Nov 10 '15 at 22:56

$$\sum_{i=1}^x{i}=\frac{x(x+1)}{2}.$$
Now, set $x=n^2-1$, and it follows that
The first index adds nothing, so you have $$\sum_{i=0}^{n^2-1}i=\sum_{i=1}^{n^2-1}i=\frac{(n^2-1)n^2}2.$$