Prove the following by the principle of mathematical induction:`\ (a b)^n=a^n b^n` for all `n in Ndot`

Prove the following by the principle of mathematical induction: (ab)^(n)=a^(n)b^(n) for all n in N.

Prove the following by the principle of mathematical induction: 1+2+2^(7)=2^(n+1)-1 for all n in N

Prove the following by the principle of mathematical induction: n^3-7n+3 is divisible 3 for all n in Ndot

Prove the following by the principle of mathematical induction: n^3-7n+3 is divisible 3 for all n in N .

Prove the following by the principle of mathematical induction: 3^(2n)+7 is divisible by 8 for all n in Ndot

Prove the following by the principle of mathematical induction: n^(3)-7n+3 is divisible 3 for all n in N.

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

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

Prove the following by the principle of mathematical induction: \ 5^(2n)-1 is divisible by 24 for all n in Ndot

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