Q. Let $P(n):n^{2} + n + 1$ is an even integer. If $P(k)$ is assumed true $\Rightarrow P(k + 1)$ is true. Therefore, $P(n)$ is true
A) For $n > 1$
B) For all $n \in N$
C) For $n > 2$
D) None of these
Explanation
(d)
Given, $P(n):n^{2} + n + 1$
At $n = 1,\ P(1)\ :3,$ which is not an even integer.
$\therefore P(1)$ is not true (Principle of Induction is not applicable).
Also, $n(n + 1) + 1$ is always an odd integer.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.