On principle of mathematical induction

Using principle of mathematical induction prove that sqrt(n) =2

Prove by using principle of mathematical induction :2^(n)<3^(n),n in N

Using principle of mathematical induction, prove the following 1+3+5+...+(2n-1)=n^(2)

Prove the rule of exponents (ab)^(n)=a^(n)b^(n) by using principle of mathematical induction for every natural number.

Using principle of mathematical induction prove that x^(2n)-y^(2n) is divisible by x+y for all nN.

By using principle of mathematical induction, prove that 2+4+6+….2n=n(n+1), n in N

Using principle of mathematical induction, prove that for all n in N, n(n+1)(n+5) is a multiple of 3.

First principle of mathematical induction

Prove by the principle of mathematical induction that n<2^(n) for alln in N