Find the sum of the infinite geometric series.
\[
1+\frac{1}{5}+\frac{1}{25}+\frac{1}{125}+\cdots
\]
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. The sum of the series is $S=\square$. (Type an integer or a simplified fraction.)
B. The series does not have a sum.
Answer
Final Answer: The sum of the series is \(\boxed{\frac{5}{4}}\)
Step 1 ：This is a geometric series with first term a = 1 and common ratio r = 1/5.
Step 2 ：The sum of an infinite geometric series can be found using the formula \(S = \frac{a}{1 - r}\), where S is the sum of the series, a is the first term, and r is the common ratio.
Step 3 ：In this case, a = 1 and r = 1/5, so we can substitute these values into the formula to find the sum of the series.
Step 4 ：\(S = \frac{1}{1 - \frac{1}{5}}\)
Step 5 ：\(S = \frac{5}{4}\)
Step 6 ：Final Answer: The sum of the series is \(\boxed{\frac{5}{4}}\)
