P(n) is the statement :`"n^2-n+7` is a prime number"(ii)Can you say that P(n) will be true for all natural numbers?give reason.

If P(n) is the statement '4n<2^n'(ii)Can you say that P(n) will be true for all natural numbers?Give reason.

P(n) is the statement : "n^2-n+7 is a prime number"(i)Verify that P(1),P(2),P(3) and P(4) are true.

Let P(n) denotes the statement 2^n gt n and if P(n) is true, show that P(n+1) is also true

Given P(n):3^(2n) 1 is divisible by 8. Is the statement P(n) true for all natural numbers? Justify your answer.

Consider the statement P(n):n(n+1)(2n+1) is divisible by 6. By assume that P(k) is true for a natural number k, Verify that P(k+1) is true.

Consider the following statement: P(n):a+ar+ar^2+……+ar^(n-1)=(a(r^n-1))/(r-1) Hence by using the principle of mathematical induction, prove that P(n) is true for all natural numbers n .

Let P(n) denotes the statement n^3+(n+1)^3+(n+2)^3 is a multiple of 9 Prove that P(1) is true

Prove that (1+x)^n ge1+n x , for all natural number 'n', where x gt-1 .

If P(n) is the statement n(n+1) is even then what about P(6)?