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im trying to find out how to get the inverse of the series 1/1+1/2+1/3+1/4....

i know the output of 30 is approximately 3.99 and 450 is around 6.6, but I'd like to be able to find the fraction range for outputs of numbers such as 10, 20, and 72. The online series calculators tend to die around output 14. My knowledge of integrals and series is weak at best.

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# ? Inverse Series method?

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