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KVPY2014MathematicsSequences and Series

Suppose a₂, a₃, a₄, a₅, a₆, a₇ are are integers such that 5 7 = a₂ 2 ! + a₃ 3 ! + a₄ 4 ! + a₅ 5 ! + a₆ 6 ! + a₇ 7 ! where 0 a < j for j=2,4,5,6,7 . The sum a₂+a₃+a₄+a₅+a₆+a₇ is

Options

  1. A8
  2. B9
  3. C10
  4. D11

Correct answer

B. 9

Step-by-step solution

5 7 = 2520 a₂+840 a₃+210 a₄+42 a₅+7 a₆+a₇ L 7 2520 a₂+840 a₃+210 a₄+42 a₅+7 a₆+a₇=3600 Let a₂=a₃=a₄=1 a₅=0 a₆=4 a₇=2

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