Question

Let $P\left(n\right)=n(n+1)$ is an even number, then which of the following satisfy $P\left(n\right)$

• A. $P\left(3\right)$
• B. $P\left(100\right)$
• C. $P\left(50\right)$
• D. All of these

Answer 1

The correct option is D All of these

Given, $P\left(n\right)=n(n+1)$

$\therefore P\left(3\right)=3.4=12\left(even\right)$

$P\left(100\right)=100\times 101=10100\left(even\right)$

$P\left(50\right)=50\times 51=2520\left(even\right)$

As $P\left(3\right),P\left(100\right),P\left(50\right)$ are even numbers.

Short cut Method: $P\left(n\right)=n(n+1)$

Product of two consecutive integer (natural numbers) is always even.