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CAT 2024 Set-2 | Quantitative Aptitude | Question: 6

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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

  1. $\frac{5}{408}$
  2. $\frac{5}{816}$
  3. $\frac{7}{408}$
  4. $\frac{7}{816}$

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