Question

The arithmetic mean of the squares of first $n$ natural numbers is :

• A. $\frac{n+1}{6}$
• B. $\frac{(n+1)(2n+1)}{6}$
• C. $\frac{n^2-1}{6}$
• D. None of these

Answer 1

Answer: (B)

$\frac{(n+1)(2n+1)}{6}$

Arithmetic mean of squares of first $n$ natural number is,
$=\frac{1^2+2^2+3^2+4^2+...........+n^2}{n}=\frac{\sum n^2}{n}=\frac{n(n+1)(2n+1)}{6n}=\frac{(n+1)(2n+1)}{6}$