Prove that `(1+x)^n ge1+n x`, for all natural number 'n', where `x gt-1`.

Prove that 2^n gt n for all positive integtrs n.

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

If A{ x: x is a natural number,x 7} , then n(A) is

Consider the following statement: P(n):a+ar+ar^2+……+ar^(n-1)=(a(r^n-1))/(r-1) Hence by using the principle of mathematical induction, prove that P(n) is true for all natural numbers n .

Consider the set {x : x= 2^n ,n is a natural number, n le5 } Write this set in roster form.

Consider the statement: P(n)=1^3+2^3+3^3+……..+n^3=[(n(n+1))/2]^2 Is P(n) true for all natural number n ? Why?

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

Consider the statement '' P(n):x^n-y^n is divisible by x-y ''. Using the principal of Mathematical induction verify that P(n) is true for all natural numbers.