Answer
$\frac{1}{4}$
Work Step by Step
1. We can identify the sequence as geometrical with $a_1=\frac{1}{5}, r=\frac{1}{5}$
2. We have $\sum_{k=1}^{\infty}5^{-k}=\frac{1}{5}\times\frac{1}{1-\frac{1}{5}}=\frac{1}{4}$
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