The continued product `2.6.10.4…..`(`n` times) in equal to

Options

A. `.^(2n)C_(n)`
B. `.^(2n)P_(n)`
C. `(n + 1)(n + 2)(n + 3) …….(n + n)`
D. `4^(n)`

Answer

B, C

Explanation

`E = 2.6.10.14….`
`=2^(n)[1,3,5,7…..]`
`= (2^(n)[1,2,3…..2n])/(2.4.6(2n-2)(2n)) = (2^(n).(2n)!)/(2^(n).n!) = .^(2n)P_(n)(B)`
Also `(2n!)/(n!) = ((1.2.3…….n)(n+1)(n+2)….2n)/(n!) :.` (C)