The value of $\frac{1}{1 ! 50 !}+\frac{1}{3 ! 48 !}+\frac{1}{5 ! 46 !}+\ldots .+\frac{1}{49 ! 2 !}+\frac{1}{51 ! 1 !}$ is $.............$.

  • [JEE MAIN 2023]
  • A

    $\frac{2^{50}}{50 !}$

  • B

    $\frac{2^{50}}{51 !}$

  • C

    $\frac{2^{51}}{51 !}$

  • D

    $\frac{2^{51}}{50 \text { ! }}$

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