Question

Question #7ea37

Answer 1

`frac{(2n+1)!}{(2n-1)!}`

Expand the factorial in the numerator:

=`frac{(2n+1)(2n)color(blue)((2n-1)!)}{color(blue)((2n-1)!)}`

`=(2n+1)(2n)`

`=2(2n+1)(n)`

Answer 2

`((2n+1)!)/((2n-1)!) = color(green)(4n^2+2n)`

Explanation:

`((2n+1)!)/((2n-1)!)`

`color(white)("XXX")=((2n+1) * (2n) * cancel((2n-1)) * cancel((2n-2)) * cancel((2n-3)) * ... * cancel(2) * cancel(1))/(cancel((2n-1)) * cancel((2n-2)) * cancel((2n-3)) * ... cancel(2) * cancel(1))`

`color(white)("XXX")=(2n+1) * (2n)`

`color(white)("XXX")=4n^2+2n`