Chapter 5.3, Problem 192E

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

192. [T] Suppose a computer can sum one million terms per second of the divergent series ${\displaystyle \underset{n=1}{\overset{N}{\sum }}\frac{1}{n}}$ -. Use the integral

test to approximate how many seconds it will take to add up enough terms for the partial sum to exceed 100.