Chapter 8, Problem 1CR

To determine

To find:

The first five terms of the sequence.

Answer to Problem 1CR

The first five terms are $\frac{2}{3}$ , $\frac{4}{5}$ , $\frac{8}{9}$ , $\frac{16}{17}$ , $\frac{32}{33}$ .

Explanation of Solution

Given information:

  $a_n=\frac{2^n}{2^n+1}$

Concept used:

For finding the first five terms of the sequence use $n$ equal to $1$ , $2$ , $3$ , $4$ and $5$ in the general form of the $n\text{th}$ term given by $a_n=\frac{2^n}{2^n+1}$ .

Calculation:

Substitute $n=1$

  $\begin{array}{c}{a}_1=\frac{2^1}{2^1+1}\\ =\frac{2}{3}\end{array}$

Substitute $n=2$

  $\begin{array}{c}{a}_2=\frac{2^2}{2^2+1}\\ =\frac{4}{5}\end{array}$

Substitute $n=3$

  $\begin{array}{c}{a}_3=\frac{2^3}{2^3+1}\\ =\frac{8}{9}\end{array}$

Substitute $n=4$

  $\begin{array}{c}{a}_4=\frac{2^4}{2^4+1}\\ =\frac{16}{17}\end{array}$

Substitute $n=5$

  $\begin{array}{c}{a}_5=\frac{2^5}{2^5+1}\\ =\frac{32}{33}\end{array}$

Hence, the first five terms are $\frac{2}{3}$ , $\frac{4}{5}$ , $\frac{8}{9}$ , $\frac{16}{17}$ , $\frac{32}{33}$ .