The sum of the infinite series \frac{1}{5}\left(\frac{1}{5}-\frac{1}{7}\right)+\left(\frac{1}{5}\right)^2\left(\left(\frac{1}{5}\right)^2-\left(\frac{1}{7}\right)^2\right)+\left(\frac{1}{5}\right)^3\left(\left(\frac{1}{5}\right)^3-\left(\frac{1}{7}\right)^3\right)+\cdots is equal to

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CAT 2024 Slot 2 QA · Question 8

The sum of the infinite series $\frac{1}{5} (\frac{1}{5} - \frac{1}{7}) + (\frac{1}{5})^{2} ((\frac{1}{5})^{2} - (\frac{1}{7})^{2}) + (\frac{1}{5})^{3} ((\frac{1}{5})^{3} - (\frac{1}{7})^{3}) + \dots$ is equal to

A.
$\frac{5}{408}$
B.
$\frac{7}{816}$
C.
$\frac{7}{408}$
D.
$\frac{5}{816}$

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