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Number Theory

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Compute a Finite Double Sum:$\sum_{i = 1}^{m} \sum_{j = 1}^{n}ij$

NUMTH-B$LWNR

Let $m , n \in \mathbb{N}$.

What is $\sum_{i = 1}^{m} \sum_{j = 1}^{n} ij$?

A

$\cfrac{m(m + 1) + n(n + 1)}{2}$

B

$\cfrac{m(m + 1)n(n + 1)}{4}$

C

$\cfrac{m(m + 1)n(n + 1)}{2}$

D

$m!~n!$