Let $\frac{1}{{{x_1}}},\frac{1}{{{x_2}}},\frac{1}{{{x_3}}},.....,$  $({x_i} \ne \,0\,for\,\,i\, = 1,2,....,n)$  be in $A.P.$  such that  $x_1 = 4$ and $x_{21} = 20.$ If $n$  is the least positive integer for which $x_n > 50,$  then $\sum\limits_{i = 1}^n {\left( {\frac{1}{{{x_i}}}} \right)} $  is equal to.

  • [JEE MAIN 2018]
  • A

    $3$

  • B

    $\frac {13}{8}$

  • C

    $\frac {13}{4}$

  • D

    $\frac {1}{8}$

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