This geometric series is the sum of two geometric series:
Sum of geometric series:
\(\frac{2}{5} + \frac{2}{5^3}+ \frac{2}{5^5}\) + ...... ∞
Here, a = \(\frac{2}{5}\)
Sum of geometric series :
\(\frac{3}{5^2} + \frac{3}{5^4} + \frac{4}{5^6} + ...... \infty\)
Here, a = \(\frac{3}{5^2}\)
∴Sum of the given infinite series = sum of both the series \(\frac{5}{12} + \frac{1}{8} = \frac{(5\times 2) + (1 \times 3)}{24}\)