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

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

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

Prove the following by using the principle of mathematical induction for all n in N : 10^(2n-1)+1 is divisible by 11.

Prove the following by using the principle of mathematical induction for all n in N : n(n + 1) (n + 5) is a multiple of 3.

Prove the following by using the principle of mathematical induction for all n in N : n(n + 1) (n + 5) is a multiple of 3.

Prove the following by using the principle of mathematical induction for all n in N :- n(n +1) (n + 5) is a multiple of 3.

Prove the following by using the principle of mathematical induction for all n in N : x^(2n)-y^(2n) is divisible by x + y .

Prove the following by using the principle of mathematical induction for all n in N :- x^(2n)-y^(2n) is divisible by x + y .

Prove the following by using the principle of mathematical induction for all n in N :- 3^(2n+2)-8n -9 is divisible by 8.

Prove the following by using the principle of mathematical induction for all n in N : 3^(2n+2)-8n-9 is divisible by 8.