Let $\frac{1}{x_1}, \frac{1}{x_2},\dots ,\frac{1}{x_n}(x_i\ne 0$ for $i=1, 2,\dots ., n)$ 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 $\sum _{i=1}^n\left(\frac{1}{x_i}\right)$ is equal to

• A

  $3$
• B

  $\frac{1}{8}$
• Correct answer
  C

  $\frac{13}{4}$
• D

  $\frac{13}{8}$

Hence, the correct answer is option: 'C'.