Question

If n be any integer, then \(n(n+1)(2n+1)\) is:

• A. odd number
• B. integral multiple of 6
• C. perfect square
• D. does not necessarily have any of the foregoing proof

Hint:

Product of three consecutive integers is divisible by 6.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Sum of squares of first n natural numbers.
Step 2: Detailed Explanation:
\(\frac{n(n+1)(2n+1)}{6}\) is sum of squares, which is integer.
So \(n(n+1)(2n+1)\) is divisible by 6.
Step 3: Final Answer:
Integral multiple of 6.