Consider the statement
`P(n)=3^(2n+2)-8n-9` is divisible by 8
Prove the statement using the principle of mathematical induction for all natural numbers.

Consider the statement P(n)=3^(2n+2)-8n-9 is divisible by 8 Verify the statement for n=1.

Consider the statement '' 7^n-3^n is divisible by 4'' Prove the statement using mathematical induction.

Consider the statement '' P(n):x^n-y^n is divisible by x-y ''. Using the principal of Mathematical induction verify that P(n) is true for all natural numbers.

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

Consider the statement P(n):n(n+1)(2n+1) is divisible by 6. Verify the statement for n=2.

(b)Prove the following by using the principle of mathematical induction for all n in N:n^2+n is even.

Consider the statement P(n):7^n-3^n is divisible by 4. Show that P(1) is true.

(b)Prove by the principle of mathematical induction that 3^n>2^n.

Consider the statement P(n):7^n-3^n is divisible by 4. Verify, by the method of mathematical induction, that P(n) is true for all natural numbers.

Consider the statement P(n):2^(3n) -1 is divisible by 7 Is the statement p(1) true? justify your answer