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The sums of powers, \( \sum_{k=1}^{n} k^a \), can be computed more efficiently if we have a closed formula for them. Sum of powers for a = 1, 2, 3 $$ \sum_{k=1}^{n} k = \frac{n(n+1)}{2} $$ One [intuitive] derivation is presented at brilliant.org : $$ S_n = 1 + 2 + 3 + … + n $$ … can be reordered as: $$ S_n = n + (n-1) + (n-2) + … + 1 $$...