Chapter 8.1, Problem 5E

To determine

To Find: The formula for the general term $a_n$ of the sequence for the sequence $\left\{1,\frac{1}{3},\frac{1}{5},\frac{1}{7},\frac{1}{9},\mathrm{...}\right\}$ .

Answer to Problem 5E

The sequence is $\frac{1}{2n+1}$ .

Explanation of Solution

Calculation:

Consider the given sequence is,

  $\left\{1,\frac{1}{3},\frac{1}{5},\frac{1}{7},\frac{1}{9},\mathrm{...}\right\}$

Consider the first term is 1.

The second term is,

  $\frac{1}{2+1}$

The second term is,

  $\frac{1}{2\left(2\right)+1}$

The third term is,

  $\frac{1}{2\left(3\right)+1}$

Thus, the sequence is,

  $\frac{1}{2n+1}$