Teams X and Y enter a sudden-death shootout after tying in a game. The teams take turns attempting shots, and the first team to score wins the shootout. Each team has a $\frac{1}{5}$ chance of scoring on their attempt, and Team X shoots first. The probability that Team X eventually wins can be expressed as the series $\sum _{k=0}^{\infty }\frac{1}{5}{\left(\frac{4}{5}\right)}^{2k}$. Find the value of this series.