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

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

  1. A

    n+12

  2. B

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

  3. C

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

  4. D

    n(n+1)2

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    Solution:

    The required mean is given by

    X¯=112+222+332++nn212+22++n2=Σn3Σn2

     X¯=n (n+1) 22n(n+1)(2n+1)6=3n(n+1)2(2n+1)

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