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

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

(b)Prove by the principle of mathematical induction that 3^n>2^n.

(a)Prove by the principle of mathematical induction that log x^n=nlogx .

Prove by the principle of mathematical induction that. 4^n+15n-1 is a mulitple of 9 for all n in N .

Prove by the principle of mathematical induction that for all n in N. (2^(3n)-1) is divisible by 7 for all n in N .

Prove by the principle of mathematical induction that for all n in N. 5^(2n)-1 is divisible by 24 for all n in N .

Prove by the principle of mathematical induction that for all n in N. 3^(2n)+7 is divisible by 8 for all n in N .

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