Home
Class 11
MATHS
Prove that (n !)^2 < n^n n! < (2n)!, for...

Prove that `(n !)^2` < `n^n n!` < `(2n)!`, for all positive integers n.

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that (2n)^2 where n in N can be expressed as the sum of n terms of a series of integers in AP

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

Prove that n! (n+2) = n! +(n+1)! .

Prove that ((n + 1)/(2))^(n) gt n!

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

Prove that 2^(n)>n,n in N

Prove that ((2n+1)!)/(n!)=2^(n)[1.3.5.....(2n-1)*(2n+1)]

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

Prove that P(n,n)=2.P(n,n-2)

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