Chapter 11.1, Problem 92E

To determine

(a)

The values of $c_1,c_2,c_3,c_4$

To determine

(b)

The mathematical proof of the given value by using a comparison of rectangles with the area under $y=x^{-1}$ over the interval [n, 2n],

${\displaystyle \underset{n}{\overset{2n}{\int }}\frac{dx}{x}+\frac{1}{2n}}\le c_n\le {\displaystyle \underset{n}{\overset{2n}{\int }}\frac{dx}{x}+\frac{1}{n}}$ where $c_n=\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}+\mathrm{...}+\frac{1}{2n}$.

To determine

(c)

The value of $\underset{n\to \infty }{\lim }{c}_n$ using the Squeeze Theorem.