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

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?

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

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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.

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

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