+0

# Series

0
124
1

Calculate the sum of the geometric series 1 + 1/5^2 + 1/5^4 + .... Express your answer as a common fraction.

Dec 31, 2021

$$1+\frac{1}{5^2}+\frac{1}{5^4}+ \mbox{ } ... \mbox{ } = \displaystyle\sum_{n=1}^{\infty} 5^{-2(-1+n)} = \frac{25}{24}$$ .