# Summation starting from 0

$$\sum_{i=0}^{n}(i)$$

This seems pretty basic, but I'm starting with the subject and the only formula I have to use for these kind of problems starts the summation at 1, like this.

$$\sum_{i=1}^{n}(i)$$ = $$\frac{n(n+1)}{2}$$

Is the same formulate valid to solve summation starting with 0? If not, how do you solve this?

• What term do you include in the summation when $i = 0$? Jan 28 at 17:50

You're asking whether $$1+2+3+\cdots+n$$ has the same value as $$0+1+2+3+\cdots+n$$ And the answer is that of course those are the same.
Yes, the formula is the same, since $$\sum_{i=0}^{n} i = 0+1+\cdots+n = 0+(1+\cdots+n) = 0 + \sum_{i=1}^n i.$$