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KVPY2012MathematicsSequences and Series

For 2²+4²+6²+ +(2 n )² 1²+3²+5²+ .+(2 n -1)² to exceed 1.01 , the maximum value of n is -

Options

  1. A99
  2. B100
  3. C101
  4. D150

Correct answer

D. 150

Step-by-step solution

array l 2² (1²+2²+3²+ + n ² ) [1²+2²+3²+ . .+(2 n )² ]-2 (1+2²+3²+ . n ² ) 2² n ( n +1)(2 n +1) 6 2 n (2 n +1)(4 n +1) 6 - 2² n ( n +1)(2 n +1) 6 >1.0 array l 2 n +2 2 n -1 array 1+ 3 2 n -1 >1.01 2 n -1>300 n < 150.5 array

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