For a positive integer $n,\left(1+\frac{1}{x}\right)^{n}$ is expanded in increasing powers of $x$. If three consecutive coefficients in this expansion are in the ratio, $2: 5: 12,$ then $n$ is equal to

  • [JEE MAIN 2020]
  • A

    $115$

  • B

    $128$

  • C

    $138$

  • D

    $118$

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