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16 August, 05:02

What is the sum of all positive integers that are multiples of 7 from 200 to 400?

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  1. 16 August, 05:23
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    203 + 210 + 217 + ... + 392 + 399 =

    = 7 (29 + 30 + 31 + ... + 56 + 57)

    = 7 (1 + 28 + 2 + 28 + 3 + 28 + ... + 28 + 28 + 29 + 28)

    = 7 (1 + 2 + 3 + ... + 28 + 29 + 28 * 29)

    = 7 (1 + 2 + 3 + ... + 28 + 29 + 812)

    = 7 * 812 + 7 * (1 + 2 + ... + 28 + 29)

    = 5684 + 7 * (29 * 30) / 2

    = 5684 + 3045

    = 8729
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