Q. If $P(n):2 + 4 + 6\ldots + (2n),\ n \in N,$ then $P(k) = k(k + 1) + 2implies$ $P(k) = (k + 1)(k + 2) + 2$ is true for all $k \in N.$ So, statement $P(n) = n(n + 1) + 2$ is true for
A) $n \geq 1$
B) $n \geq 2$
C) $n \geq 3$
D) None of these
Explanation
(d)
Here, $P(1) = 2$ and from the equation
$\ \ \ \ \ \ \ \ \ \ \ P(k) = k(k + 1) + 2$
$\Longrightarrow \ \ \ \ P(1) = 4$
So, $P(1)$ is not true
Hence, mathematical induction is not applicable.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.