Question

The weighted mean of first n natural numbers whose weights are equal to the squares of corresponding numbers is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$Weightedmean=\frac{{1.1}^2+{2.2}^2+....+n.n^2}{1^2+2^2+...+n^2}$
$=\frac{\sum n^3}{\sum n^2}=\frac{\frac{n(n+1)}{2}\frac{n(n+1)}{2}}{\frac{n(n+1)(2n+1)}{6}}=\frac{3n(n+1)}{2(2n+1)}.$