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Manipal MET2019MathematicsBinomial Theorem

The remainder obtained when 1!+2!+ +200! is divided by 14 is

Options

  1. A3
  2. B4
  3. C5
  4. DNone of the above

Correct answer

C. 5

Step-by-step solution

aligned & (1!+2!+3!+4!+5!+ +200!) 14 & =1+2+6+24+120+720+(14 M) & =873+14 M=5+868+14 M & =5+14 62+14 M=5+14(62+M) aligned Hence, when 1!+2!+ +200 ! is divided by 14 , remainder is 5 .

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