Chapter 3, Problem 23P

To determine

(a)

The authenticity of the statement “Sum of the infinite series ${\displaystyle \sum _{n=1}^{\infty }\frac{{\left(9/10\right)}^n}{n}}$ converges to $\ln 10$ ” using MATLAB; a vector $n$ in which the first element is $1$, the increment is $1$ and the last term is $10$; a vector in which the elements are $\frac{{\left(9/10\right)}^n}{n}$ using element-by-element calculations and MATLAB’s built-in function $\text{sum}$ to sum the series; the comparison of these values to $\ln 10$. (use format long to display the numbers.)

To determine

(b)

The authenticity of the statement “Sum of the infinite series ${\displaystyle \sum _{n=1}^{\infty }\frac{{\left(9/10\right)}^n}{n}}$ converges to $\ln 10$ ” using MATLAB; a vector $n$ in which the first element is $1$, the increment is $1$ and the last term is $50$; a vector in which the elements are $\frac{{\left(9/10\right)}^n}{n}$ using element-by-element calculations and MATLAB’s built-in function $\text{sum}$ to sum the series; the comparison of these values to $\ln 10$. (use format long to display the numbers.)

To determine

(c)

The authenticity of the statement “Sum of the infinite series ${\displaystyle \sum _{n=1}^{\infty }\frac{{\left(9/10\right)}^n}{n}}$ converges to $\ln 10$ ” using MATLAB; a vector $n$ in which the first element is $1$, the increment is $1$ and the last term is $100$; a vector in which the elements are $\frac{{\left(9/10\right)}^n}{n}$ using element-by-element calculations and MATLAB’s built-in function $\text{sum}$ to sum the series; the comparison of these values to $\ln 10$. (use format long to display the numbers.)