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prove that for all odd k
(1k + 2k + 3k + ... + nk) is divisible by n(n+1)/2.
you may use principal of mathematical induction.
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7 Answers
11
3a hint.
S = (1^k + 2^k + 3^k + ... + n^k).
2S = (1^k + 2^k + 3^k + ... + n^k) + (n^k + (n-1)^k + ....... + 2^k + 1^k).
then use the fact (n^k) + (m^k) is divisible by (n+m) for odd k.
