If `P(n)` is the statement `n^2-n+41` is prime. Prove that `P(1),\ P(2)a n d\ P(3)` are true. Prove also that `P(41)` is not true.

If P(n) is the statement n^(2)-n+41 is prime. Prove that P(1),P(2) and P(3) are true. Prove also that P(41) is not true.

Let P(n) be the statement " n^2-n+41 " is prime. Prove that P(1), P(2) and P(3) are true. Also prove that P(41) is not true. How does this not contradict the Principle of Induction ?

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.

If P (n) is the statement : "2^(3n)- 1 is an integral multiple of 7”, prove that P(1), P(2) and P (3) are true.

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 divisible is 12 prove that the statements P(3) and P(4) are true,but that P(5) is not true.

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

If P(n) be the statement " 10n+3 is a prime number", then prove that P(1) and P(2) are true but P(3) is false.

if P(n) be the statement 10n+3 is a prime number", then prove that P(1) and P(2) are true but P(3) is false.

If P(n) is the statement n^3+n is divisible by 3, prove that P(3) is true but P(4) is not true.