Prove that `((2n+1)!)/(n !)=2^n{1. 3. 5 (2n-1)(2n+1)}`

Prove that: :((2n)!)/(n!)={1.3.5...(2n-1)}2^(n)

Prove that: :2^(n)C_(n)=(2^(n)[1.3.5(2n-1)])/(n!)

Prove that ((2n)!)/(n!) =2^(n) xx{1xx3xx5xx...xx(2n-1)}.

Prove that .^(2n)C_(n)=(2^(n)xx[1*3*5...(2n-1)])/(n !) .

Prove that ((4n)C_(2n))/((2n)C_(n))=(1.3.5...(4n-1))/([1.3.5...(2n-1)]^(2))

If n is a positive integer,prove that 1-2n+(2n(2n-1))/(2!)-(2n(2n-1)(2n-2))/(3!)+...+(-1)^(n-1)(2n(2n-1)...(n+2))/((n-1)!)=(-1)^(n+1)(2n)!/2(n!)^(2)

Prove that ((2n)!)/(2^(2n)(n!)^(2))<=(1)/(sqrt(3n+1)) for all n in N

Prove that (2^(n)+2^(n-1))/(2^(n+1)-2^(n))=(3)/(2)

For n in N, prove that (n+1)[n!n+(n-1)!(2n-1)+(n-2)!(n-1)]=(n+2)!

Prove that :1+2+3+...+n=(n(n+1))/(2)