Prove by mathematical induction that, `2n+7lt(n+3)^(2)` for all `ninNN`.

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

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

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

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

Prove by the principle of mathematical induction that for all n in N,3^(2n) when divided by 8, the remainder is always 1.

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

Using the principle of mathematical induction, prove that (n^(2)+n) is seven for all n in N .

Prove by the principle of mathematical induction that for all n in N:1^(2)+2^(2)+3^(2)+...+n^(2)=(1)/(6)n(n+1)(2n+1)

Using the principle of mathematical induction prove that (1+x)^(n)>=(1+nx) for all n in N, where x>-1

Prove by the principle of mathematical induction that n(n+1)(2n+1) is divisible by 6 for all n in N