Math CentralQuandaries & Queries


Question from Mohd, a student:
you explained the way of getting the summation of 100 series numbers but what is the summation of the numbers 1/1+1/2+1/3+1/4+1/5.............................+1/100


That is not a question that has a very tidy answer! It can be estimated in various ways, for instance (see below)

or given by a series that starts

gamma + ln(100) + 1/200 - 1/120000 + 1/12000000000 +...

where gamma is the Euler-Mascheroni constant 0.5772156649...

and the sum is about 5.18739418. The first three terms are exact enough for most purposes.

Good Hunting!

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