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

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

Prove the following by the principle of mathematical induction: ((2n)!)/(2^(2n)(n!)^(2))<=(1)/(sqrt(3n+1)) for all n in N

Prove that ((2n)!) / (n!) = 2^n(2n - 1) (2n - 3) ... 5.3.1.

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

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

Prove that (^(2n)C_0)^2+(^(2n)C_1)^2+(^(2n)C_2)^2-+(^(2n)C_(2n))^2-(-1)^n^(2n)C_ndot

Prove that (^(2n)C_0)^2-(^(2n)C_1)^2+(^(2n)C_2)^2-+(^(2n)C_(2n))^2-(-1)^n^(2n)C_ndot

Prove that sum_(r=0)^(2n)(.^(2n)C_(r))^(2)=n^(4n)C_(2n)