[" Let "x_(n)=(2^(n)+3^(n))^(1/2n)" for all natural numbers "n" ."],[" Then "]

Let x_(n)=(2^(n)+3^(n))^(1//2n) for all natural number n. Then

1+5+9+...+(4n-3)=n(2n-1) for all natural numbers n

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

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

Show that ^nP_n= "^nP_(n-1) for all natural numbers n .

If A = [(1,1),(1,1)] , prove by induction that A^n = [(2^(n-1), 2^(n-1)), (2^(n-1), 2^(n-1))] for all natural numbers n.

Is 2^(3-n) a prime number for all natural numbers n?

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

prove that 2+4+6+…2n=n^(2)+n , for all natural numbers n.

prove that 2+4+6+…2n=n^(2)+n , for all natural numbers n.