Chapter 11.5, Problem 34WE

(a)

To determine

To Find: The approximate value of $r^n$ .

Answer to Problem 34WE

The approximate value of $r^n$ is 0.

Explanation of Solution

Given Information:

  $\left|r\right|<1$ and $n$ is a very large integer.

Calculation:

The approximate value of $r^n$ is approximately 0 because as we know that any number between 0 and 1, when it is multiplied by itself it will give us a number that is near to 0 .

Hence, the approximate value of $r^n$ is 0.

(b)

To determine

To Find: The approximate value of $S_n$ where $S_n=\frac{t_1(1-r^n)}{1-r}$ .

Answer to Problem 34WE

The approximate value of $S_n$ is $\frac{t_1}{1-r}$ .

Explanation of Solution

Given Information:

  $\left|r\right|<1$ and $n$ is a very large integer.

Calculation:

If we try to approximately substitute $r^n$ by the value 0 then we will get

  $S_n\approx \frac{t_1(1-0)}{1-r}=\frac{t_1}{1-r}$

Thus, $\frac{t_1}{1-r}$ is the approximate value

Hence, the approximate value of $S_n$ is $\frac{t_1}{1-r}$ .