Q58 / 160 · AP EAMCET 2024 (19 May Shift 2) · Mathematics

$1-\frac{2}{3}+\frac{2.4}{3.6}-\frac{2.4 .6}{3.6 .9}+\ldots \infty=$

  • Correct answer
    A
    $\frac{3}{5}$
  • B
    $\left(\frac{2}{5}\right)^{\frac{2}{3}}$
  • C
    $\frac{2}{5}$
  • D
    $\left(\frac{3}{5}\right)^{\frac{2}{3}}$

Solution

$1-\frac{2}{3}+\frac{2 \cdot 4}{3 \cdot 6}-\frac{2 \cdot 4 \cdot 6}{3 \cdot 6 \cdot 9}+\ldots \ldots$ $=1-\frac{2}{3}+\left(\frac{2}{3}\right)^2-\left(\frac{2}{3}\right)^3+\ldots . .=\frac{1}{1+\frac{2}{3}}=\frac{3}{5}$.

Hence, the correct answer is option: 'A'.

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