Prove that `((n^(2))!)/((n!)^(n))` is a natural number for all n `in` N.

Prove by the principle of mathematical induction that (n^5)/5+(n^3)/3+(7n)/(15) is a natural number for all n in Ndot

If n is a natural number then sqrtn is

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

Prove that 4n^(2)-1 is an odd number for all n in N

Prove that (1+x)^(n) ge (1+nx) for all natural number n where x gt -1

Prove that (n !+1) is not divisible by any natural number between 2 and n

Prove that ((2n)!)/(n!) =2^(n) (1,3,5,……..(2n-1)) .

Prove that 2.7^(n)+ 3.5^(n)-5 is divisible by 24 for all n in N

Prove that 2 le (1+ (1)/(n))^(n) lt 3 for all n in N .