Problem

What is the sum of \( 1, \frac{1}{5}, \frac{1}{25}, \frac{1}{125}, \ldots ? \)

Answer

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Answer

\(S = \frac{5}{4}\)

Steps

Step 1 ：\(S = \sum_{n=0}^{\infty} \frac{1}{5^n}\)

Step 2 ：\(S = \frac{1}{1 - \frac{1}{5}}\)

Step 3 ：\(S = \frac{5}{4}\)

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