If 3 20 20 1 20 20 1 1 C , C C 21 i i i i – k = – æ ö ç ÷ = + è ø å then k equals:

Question:
If $\sum_{i=1}^{20}\left(\frac{{ }^{20} \mathrm{C}_{i-1}}{{ }^{20} \mathrm{C}_{i}+{ }^{20} \mathrm{C}_{i-1}}\right)^{3}=\frac{k}{21}$, then $k$ equals:

Correct Option: 4

JEE Main Previous Year 1 Question of JEE Main from Mathematics Permutations And Combinations chapter.