Let P(n) be a statement such that `P(n) Rightarrow P(n+1)` for all `n in NN`. Also, if P(k) is true, `k in N`, then we can conclude that.-

Let P(n) be a statement such that P(n) Rightarrow P(n+1) for all n in NN . Also P(k) is true, k in NN . Then we can conclude that:

Let P(n) be a statement and let P(n) Rightarrow P(n+1) for all natural number n, then P(n) is true.

Let P(n) be a statement and let P(n) Rightarrow P(n+1) for all natural number n, then P(n) is true.

A student was asked to prove a statement P(n) by using the principle of mathematical induction. He proved that P(n) Rightarrow P(n+1) for all n in N and also that P(4) is true: On the basis of the above he can conclude that P(n) is true.

A student was asked to prove a statement P(n) by using the principle of mathematical induction. He proved that P(n) Rightarrow P(n+1) for all n in N and also that P(4) is true: On the basis of the above he can conclude that P(n) is true.

Let P(n): n^(2)+n is odd. Then P(n) Rightarrow P(n+1) for all n in NN and P(1) is not true. From here, we can conclude that:

Let P(n): n^(2)+n is odd, then P(n) Rightarrow P(n+1) for all n. and P(1) is not true. From here, we can conclude that

If P(n) is a statement (n in N) such that if P(k) is true,P(k+1) is true for k in N, then P(k) is true.

Let P(n) be the statement : n^(2) +n is even Is P(n) true for all ninN ?