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    OlympiadMediumProofs7–9

    What is the sum of the first nn odd numbers, 1+3+5+…+(2n−1)1 + 3 + 5 + \ldots + (2n-1)?

    Qual é a soma dos primeiros nn números ímpares, 1+3+5+…+(2n−1)1 + 3 + 5 + \ldots + (2n-1)?

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    Solution

    Step 1 of 3

    1. 1.Take n2n^{2} dots arranged in an n×nn \times n square.