Chapter 4.2, Problem 51HP

To determine

To explain : the fraction is increasing or decreasing when the value of $n$ increases

Answer to Problem 51HP

The fraction is decreasing when $n$ increases.

Explanation of Solution

Given information :

The fractionis $\frac{1}{2^n}$

If we will take value of $n$ increase to increases then the value of fraction will be decrease because if $2^n$ in numerator the value of $2^n$ will be increase but here $2^n$ in denominator, so the value of $\frac{1}{2^n}$ will be decrease. By the property of fraction, if maintain the numerator and denominator will be increase, then the value of fraction will be decrease.

For Example:

  $\begin{array}{l}\frac{1}{8}<\frac{1}{2}\\ 8>2\end{array}$

In the fraction’s value will decrease.

Hence,the fraction is decreasing when $n$ increases.