Can you do it?

Algebra Level 2

1 × 1 × 1 + 2 × 2 × 2 + 3 × 3 × 3 + ⋯ + 12 × 12 × 12 = ? 1 \times 1 \times 1 + 2 \times 2 \times 2 + 3 \times 3 \times 3 + \cdots + 12 \times 12 \times 12 = \ ?

6098 6088 6083 6084

Sin Ndt by SIN NDT , 14, Vietnam

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1 solution

∑ i = 1 n i 3 = [ n ( n + 1 ) 2 ] 2 \sum_{i=1}^n i^3=\left[\dfrac{n(n+1)}{2}\right]^2 . Here n = 12 n=12 . So the sum is ( 12 × 13 2 ) 2 = 7 8 2 = 6084 \left(\dfrac{12\times 13}{2}\right)^2=78^2=\boxed {6084}

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