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Math Help - nth Partial Sums & Integral Test

  1. #1
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    nth Partial Sums & Integral Test

    Interesting problem from Strang's Calculus I'm having thoughts on.

    Every second a computer adds a million terms of the divergent series with general term 1/(n ln n) (defined for n > 1). By comparison with the associated integral, estimate the partial sum after a million years.

    I know that the number of terms counted after a million years is about 3.2 x 1019. I'm confused onto how to proceed. Are there any suggestions? Thanks for any help with such a great problem!
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  2. #2
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    Re: nth Partial Sums & Integral Test

    \int \frac{dx}{x \ln(x)} = \ln(\ln(x))

    see if that helps.
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