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

Question Number 62878 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 (n + 1)}{2}

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

= \frac{n^{2} {(n + 1)}^{2}}{4}

Commented by mathmax by abdo last updated on 26/Jun/19

t h a n k s s i r m r w .