If P`(n)` is the statement `n^2> 100"` , prove that whenever `P(r)` is true, `P(r+1)` is also true.

If P(n) is the statement 2^ngeq3n , and if P(r) is true, prove that P(r+1) is true.

If P(n) is the statement n^2+n is even, and if P(r) is true then P(r+1) is true.

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.

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(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.

Let P(n) be the statement "3^n > n" . If P(n) is true, P(n+1) is also 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 2^ngtn^n and if P(m) is true, show tht P(m+1) is also true

Let P(n) be the statement ''(3)^(n)gt n'' . If P(n) is true , prove that P(n + 1) is true.

A student was asked to prove a statement P(n) by induction. He proved that P(k+1) is true whenever P(k) is true for all k ge 5 in N and also that P(5) is true. On the basis of this he conclude that P(n) is true (i) AA n in W (ii) AA n gt 5 (iii) AA n ge 5 (iv) AA n lt 5