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Question
If 1 + 2 + 3 + ... + k = 325, then find 13 + 23 + 33 + ... + k3
Solution
1 + 2 + 3 + … + k = 325
13 + 23 + 33 + ... + k3 = `sum_1^"n" "n"^3`
= `(("n"("n" + 1))/2)^2`
= `(sum_1^"n" "n")^2`
If 1 + 2 + 3 + … + k = 325
13 + 23 + 33 + … + k3 = (325)2
= 105625
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