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Number Theory

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

NUMTH-JBS9PV

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

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

A

1

B

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

C

$mn$

D

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