Summation starting from 0

Question

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

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?

Answer 1

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.

Answer 2

Yes, the formula is the same, since $$ \sum_{i=0}^{n} i = 0+1+\cdots+n = 0+(1+\cdots+n) = 0 + \sum_{i=1}^n i. $$