Chapter 12: Q 12.53 (page 1163)

Find the sum of the infinite geometric series.
$48 + 24 + 12 + 6 + + 3 + \frac{3}{2} + . . .$

Short Answer

Expert verified

Sum is $96$ .

Step by step solution

Step 1. Given information

Infinite geometric series is $48 + 24 + 12 + 6 + + 3 + \frac{3}{2} + . . .$

Step 2.

Consider the infinite geometric series: $48 + 24 + 12 + 6 + 3 + \frac{3}{2} + . . .$

Let $a, r$ denote the first term and the common ratio respectively.

$\begin{array}{rcl} r & = & \frac{24}{48} \\ = & \frac{1}{2} \end{array}$

$S_{n} = \frac{a}{1 - r}$ where $S_{n}$ denotes the sum.

$\begin{array}{rcl} S_{n} & = & \frac{48}{1 - \frac{1}{2}} \\ = & 96 \end{array}$

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Find the sum of the infinite geometric series.
$48 + 24 + 12 + 6 + + 3 + \frac{3}{2} + . . .$

Short Answer

Step by step solution

Step 1. Given information

Step 2.

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Find the sum of the infinite geometric series.
$48 + 24 + 12 + 6 + + 3 + \frac{3}{2} + . . .$