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Question

99r=1r!(r2+r+1)=
  1. 102!100!
  2. 100(100!)1
  3. 99(100!)1
  4. 100(99!)1


Solution

The correct option is B 100(100!)1
r!(r2+r+1)=r![(r+1)2r]
=r!(r+1)(r+1)r!r
=(r+1)!(r+1)r!r
Which is of form Vr+1Vr
99r=1r!(r2+r+1)=V100V1
=(100!)1001

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