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16 September, 20:33

Find the sum of (1 - 1/n) + (1 - 2/n) + (1 - 3/n) ... upto n terms

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  1. 16 September, 20:36
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    (n-1) / 2

    Step-by-step explanation:

    We have that the sum has the form of:

    Sn = n / 2 [2 * a + (n-1) * d]

    we compute the terms of a and d

    a = 1 - 1 / n

    a = (n - 1) / n

    , that is, the first term, in the case d is the subtraction between the second and the first term, thus:

    d = 1 - 2 / n - (1 - 1 / n)

    d = 1 - 2 / n - 1 + 1 / n

    d = - 1 / n

    now if replacing these values:

    Sn = n / 2 * [2 * (n - 1) / n + (n-1) * ( - 1 / n)

    Sn = n / 2 * [2 * (n-1) - (n-1) ] / n

    Sn = 1/2 * (n-1)

    Therefore, the value of that sum is (n-1) / 2
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