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Find the value of 1+ 1 1^2 + 1 2^2 + 1+ 1 2^2 + 1 3^2 + 1+ 1 3^2 + 1 4^2 + + 1+ 1 2010^2 + 1 2011^2

Options

  1. A2011- 1 2011
  2. B2011+ 1 2011
  3. C2011- 1 2010
  4. Dnone of these

Correct answer

A. 2011- 1 2011

Step-by-step solution

T_n= 1+ 1 n^2 + 1 (n+1)^2 = n^4+2 n^3+n^2+n^2+2 n+1+n^2 n^2(n+1)^2 = n^2+n+1 n(n+1) =1+ 1 n(n+1)

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