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AP EAMCET202124 Aug 2021Morning ShiftMathematicsStatisticsActual

The mean of the squares of first n natural numbers is

Options

  1. A[ n(n+1) 2 ]^2
  2. B2 n^2-3 n+1 6
  3. C2 n^2+3 n+1 6
  4. Dn(n+1)(2 n+1) 6

Correct answer

C. 2 n^2+3 n+1 6

Step-by-step solution

First n natural numbers 1,2,3,4, , n Their squares 1^2, 2^2, 3^2, , n^2 Now mean = Sum of observations Total number of observations aligned & = 1^2+2^2+3^2+ +n^2 n & = n 6 (n+1)(2 n+1) n [ n^2= n 6 (n+1)(2 n+1) ] & = (n+1)(2 n+1) 6 = 2 n^2+3 n+1 6 aligned

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