If ${\left( {2 + \frac{x}{3}} \right)^{55}}$ is expanded in the ascending powers of $x$ and the coefficients of powers of $x$ in two consecutive terms of the expansion are equal, then these terms are

  • [JEE MAIN 2014]
  • A

    $8^{th}$ and $9^{th}$

  • B

    $7^{th}$ and $8^{th}$

  • C

    $28^{th}$ and $29^{th}$

  • D

    $27^{th}$ and $28^{th}$

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  • [JEE MAIN 2020]

Show that the middle term in the expansion of $(1+x)^{2 n}$ is
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