Prove by principle of Mathematical Induction that for all natural number in `n(n+1)(n+2)` is divisible by 6.

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

Prove by using the principle of mathematical induction that for all n in N, 10^(n)+3.4^(n+2)+5 is divisible by 9

Using the principle of Mathematical Induction, prove that forall nin N , 4^(n) - 3n - 1 is divisible by 9.

Show by using the principle of mathematical induction that for all natural number n gt 2, 2^(n) gt 2n+1

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

Using principle of mathematical induction, prove that 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 Nvdots10^(2n-1)+1 is divisible by 11.

Prove the following by using the principle of mathematical induction for all n in Nvdots3^(2n+2)-8n-9 is divisible by 8.

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