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

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n+12

3n(n+1)2(2n+1)

(n+1)(2n+1)6

n(n+1)2

answer is B.

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Detailed Solution

The required mean is given byX¯=1⋅12+2⋅22+3⋅32+…+n⋅n212+22+…+n2=Σn3Σn2⇒ X¯=n (n+1) 22n(n+1)(2n+1)6=3n(n+1)2(2n+1)

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