- #1

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The factorial is usually defined as

[tex]n! = \prod_{k=1}^n k[/tex] if k is a natural number greater than or equal to 1.

Is there an operation that is defined as

[tex]\sum_{k=0}^n k[/tex]

if one wants to find, for instance, something like 5+4+3+2+1?

I ask because I was thinking about binomial expansions and Pascal's triangle, and I'm just curious as to why the factorial operation (!) exists for products but I've never heard of such a thing for sums.