Let P(n) be the statement `n2 + n is even’. If P(k) is true , then show that P(k + 1) is true.

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

We are given that P(k) is true.
i.e. `k2 + k is even’
Let k2 + k = 2q,                       q N
Let n = k + 1
 (k + 1)2 + k + 1 = (k + 1)(k + 1) + k +1 = k(k + 1) + 2(k + 1)
                              = 2q + 2(k + 1), which is even.
Thus P(k +1) is true, whenever P(k) is true.

Answered by  | 4th Jun, 2014, 03:23: PM