If `P(n) is the statement 4n<2^n`(i)Verify that `P(1),P(2),P(3),P(4) and P(5)` are true.

If P(n) is the statement n(n+1)(n+2) is divisiblé by 12, prove that P(3) and P(4) are true, but P(5) is not true

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

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.

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.

Let P(n) be the statement "n+3" is prime. Is P(3) true? What is your opinion when n=4?

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

Let P(n) denotes the statement n^3+(n+1)^3+(n+2)^3 is a multiple of 9 If P(k) is true, prove that P(k+1) is also 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

Let P(n) denotes the statement '3^n gt 2^n' . Is P(1) true?

Let P(n) denotes the statement 2^(n+3) le (n+3)! Are P(1) and P(2) true? Justify your answer.