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Chapter 0: Problem 36

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$S=\frac{C}{1-r} \text { for } r$$

Short Answer

Expert verified
The variable 'r' in the given geometric series sum formula can be isolated and solved as \( r = \frac{S - C}{S} \).

Step by step solution

01

Start with the original formula

You have the formula \( S = \frac{C}{1-r} \).
02

Isolate the fraction

To isolate 'r', first get rid of the fraction. Multiply both sides of the equation by the denominator of the fraction, which is \(1-r\). This gives \( S \cdot (1-r) = C \).
03

Distribute the S

Next, you need to distribute the \(S\) on the left side of the equation, so it multiplies both \(1\) and \(-r\). This results in \( S - Sr = C \).
04

Isolate 'r'

Get 'r' alone on one side of the equation. Rearrange the equation so all terms involving 'r' are on one side, and constants are on the other side. This results in \( Sr = S - C \). To completely isolate 'r', divide both sides by \(S\), which gives: \( r = \frac{S - C}{S} \).

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