Let ${1 \over {{x_1}}},{1 \over {{x_2}}},...,{1 \over {{x_n}}}\,\,$ (xi $ \ne $ 0 for i = 1, 2, ..., n) be in A.P. such that x1=4 and x21 = 20. If n is the least positive integer for which ${x_n} > 50,$ then $\sum\limits_{i = 1}^n {\left( {{1 \over {{x_i}}}} \right)} $ is equal to :

Question

Let ${1 \over {{x_1}}},{1 \over {{x_2}}},...,{1 \over {{x_n}}}\,\,$ (x_i $ \ne $ 0 for i = 1, 2, ..., n) be in A.P. such that x₁=4 and x₂₁ = 20. If n is the least positive integer for which ${x_n} > 50,$ then $\sum\limits_{i = 1}^n {\left( {{1 \over {{x_i}}}} \right)} $ is equal to :

${1 \over 8}$

${{13} \over 8}$

${{13} \over 4}$

Solution

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