Chapter 5.3, Problem 193E

The next few exercises are intended to give a sense of applications in which partial sums of the harmonic series arise.

193. [T] A fast computer can sum one million terms pet

second of the divergent series Use the integral ${\displaystyle \underset{n=1}{\overset{N}{\sum }}\frac{1}{2\ln n}}$test to approximate how many seconds it will take to add up enough terms for the partial sum to exceed 100.