Let ${A_n} = \left( {\frac{3}{4}} \right) - {\left( {\frac{3}{4}} \right)^2} + {\left( {\frac{3}{4}} \right)^3} - ..... + {\left( { - 1} \right)^{n - 1}}{\left( {\frac{3}{4}} \right)^n}$ and $B_n \,= 1 - A_n$ . Then, the least odd natural number $p$ , so that ${B_n} > {A_n}$, for all $n \geq p$ is

  • [JEE MAIN 2018]
  • A

    $5$

  • B

    $7$

  • C

    $11$

  • D

    $9$

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