###
A note on the calculation of Euler's constant

American Mathematical Monthly, Vol. 23 (1916), p73.

Euler's constant is usually defined by the relation

In this note Horton calls attention to the fact that Euler's constant
can be calculated to several places of accuracy from an idea used in
Cauchy's integral test for a convergent series of positive monotone
decreasing terms, namely that both

and

approximate the sum of the series with an error less than
. Horton uses this to show
that

approximates Euler's constant with an error less than