Show by using the principle of mathematical induction that for all natural number `n gt 2, 2^(n) gt 2n+1`

Prove by the principle of mathematical induction that 2^ n >n for all n∈N.

Using the principle of mathematical induction, prove that n<2^n for all n in N

Prove by the principle of mathematical induction that n<2^n"for all"n in Ndot

Prove the following by using the principle of mathematical induction. n(n+1)+1 is an odd natural number, n in N .

By the principle of mathematical induction prove that for all natural numbers 'n' the following statements are true, 2+2^(2)+2^(3)+…..+2^(n)=2(2^(n)-1)

Prove by the principle of mathematical induction that for all n in N ,n^2+n is even natural number.

Prove by the principle of mathematical induction that for all n in N ,n^2+n is even natural number.

Prove the following by using the principle of mathematical induction for all n in N : (2n+7)<(n+3)^2 .

Prove by the principle of mathematical induction that for all n in N : 1+4+7++(3n-2)=1/2n(3n-1)

Prove by using the principle of mathematical induction that for all n in N, 10^(n)+(3xx4^(n+2))+5 is divisible by 9 .