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    OlympiadEasyNumber Theory10–12

    What is 1^{3} + 2^{3} + \cdots + 10^{3}?

    Quanto vale 1^{3} + 2^{3} + \cdots + 10^{3}?

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    Solution

    Step 1 of 3

    1. 1.Induction proves 1^{3} + \cdots + n^{3} = \left(\frac{n(n+1)}{2}\right)^{2}: the step needs (S_n + (n+1)^3) to equal S_{n+1}, which expands correctly.