Prove that ((n^(2))!)/((n!)^(n)) is a natural number for all n in N. | CLASS 12 | PERMUTATION AN...

Prove that (n^(5))/(5)+(n^(3))/(3)+(7n)/(15) is a natural number.

prove that n^(2)lt2^(n) , for all natural number n≥5 .

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

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

Statement 1: ((n^(2))!)/((n!)^(n)) is natural number of for all n in N Statement 2: Number of ways in which n^(2) objects can be distributed among n persons equally is (n^(2))!/(n!)^(n)

Prove that 2n +1 lt 2^(n) for all natural numbers n ge3

Prove that log_(n)(n+1)>log_(n+1)(n+2) for any natural number n>1

n^(2)+n+1 is a/an ___________ number for all n in N

prove that 2nlt(n+2)! for all natural numbers n.

Prove that (1+x)^(n)>=(1+nx) for all natural number n,where x>-1