calculus infinate sums

how many terms of the series 1/(n*(ln(n)^8)) from n=2 to infinity would you have to add to find the sum to within 0.01

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  1. You can get an idea from the continuous function
    f(x)=1/(x*(ln(x)^8))
    From:
    ∫f(x)dx from k to ∞
    =(1/7)ln(k)^7
    which gives an idea of the error if the series is summed to the kth term.

    From the result, and equating
    (1/7)ln(k)^7 = 0.01
    you should get the value of k for the required precision.

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  2. thanks that makes sense

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