calculate-min-0-i-n-and-0-j-n-i-j-

Question Number 62879 by mathmax by abdo last updated on 26/Jun/19

c a l c u l a t e m i n \sum_{0 ⩽ i ⩽ n a n d 0 ⩽ j ⩽ n} (i + j)

Answered by mr W last updated on 26/Jun/19

\sum_{0 ⩽ i ⩽ n a n d 0 ⩽ j ⩽ n} (i + j)

= \sum_{0 ⩽ i ⩽ n} \sum_{0 ⩽ j ⩽ n} (i + j)

= \sum_{0 ⩽ i ⩽ n} (i + \frac{n (1 + n)}{2})

= \frac{n (n + 1)}{2} + \frac{n (1 + n)}{2}

= n (n + 1)

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