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JEE Advanced2008MathematicsDefinite IntegrationActual

Let S_n= _ k=0 ^n n n^2+k n+k^2 and T_n= _ k=0 ^ n-1 n n^2+k n+k^2 , for n=1,2,3, , then

Options

  1. AS_n < 3 3
  2. BS_n> 3 3
  3. CT_n < 3 3
  4. DT_n> 3 3

Correct answer

A. S_n < 3 3

Step-by-step solution

Given, aligned S_n & = _ k=0 ^n n n^2+k n+k^2 & = _ k=0 ^n 1 n ( 1 1+ k n + k^2 n^2 ) 3 3 .

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