If ${s_n} = 1 + \frac{1}{2} + \frac{1}{{{2^2}}} + ........ + \frac{1}{{{2^{n - 1}}}}$ , then the least integral value of $n$ such that $2 - {s_n} < \frac{1}{{100}}$ is

  • A

    $7$

  • B

    $9$

  • C

    $8$

  • D

    $6$

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