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JEE Main201912 Apr 2019Morning ShiftMathematicsFunctionsActual

For x ∈ R , Let [ x ] denotes the greatest integer ≤ x , then the sum of the series - 1 3 + - 1 3 - 1 100 + - 1 3 - 2 100 + . . . . . + - 1 3 - 99 100 is

Options

  1. A- 131
  2. B- 153
  3. C- 135
  4. D- 133

Correct answer

D. - 133

Step-by-step solution

Greatest integer function f x = x = 0                             ;   0 ≤ x < 1 - 1                               ;   - 1 ≤   x   < 0 - 2                                       ;   - 2 ≤ x < - 1 Given series S = - 1 3 + - 1 3

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