Prove that the inequality `|sinn x|len|sinx|` is valid for all positive integers `n`

Prove that 2^n > n for all positive integers n.

Prove by induction the inequality (1+x)^ngeq 1+n x whenever x is positive and n is a positive integer.

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

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

Using binomial theorem, prove that 5^(4n)+52n-1 is divisible by 676 for all positive integers n.

Prove that the function f(x)=x^n is continuous at x = n , where n is a positive integer.

Let p(n) = (n+1)(n+3) (n+5)(n+7)(n+9) . What is the largest integer that is a divisor of p(n) for all positive even integers n ?

Using mathematical induction prove that d/(dx)(x^n)=n x^(n-1) for all positive integers n.

Prove that n^2-n divisible by 2 for every positive integer n.

Prove that the greatest integer function [x] is continuous at all points except at integer points.