발산 판정법과 적분 판정법

In certain applications of probability, such as the so-called Watterson estimator for predicting mutation rates in population genetics, it is important to have an accurate estimate of the number ${H}_{k}=\left(1+\frac{1}{2}+\frac{1}{3}+\cdots +\frac{1}{k}\right).$ Recall that ${T}_{k}={H}_{k}-\ln k$ is decreasing. Compute $T=\lim_{k\to \infty }{T}_{k}$ to four decimal places. (Hint: $\frac{1}{k+1}<{\int }_{k}^{k+1}\frac{1}{x}dx$.)