The sum of the series `1/(1!(n-1)!)+1/(3!(n-3)!)+1/(5!(n-5)!)+…..+1/((n-1)!1!)` is = (A) `1/(n!2^n)` (B) `2^n/n!` (C) `2^(n-1)/n!` (D) `1/(n!2^(n-1)`

Options

A. `(2^(n-1))/((n-1)!)`
B. `(2^(n))/((n-1)!)`
C. `(2^(n-1))/(n!)`
D. `(2^(n))/(n!)`

Answer

C