Let n=2015 The least positive integer k for which kn2n2−12n2−22n3−32…n2−(n−1)2=r!  for some positive integer r is

 Let n=2015 The least positive integer k for which kn2n212n222n332n2(n1)2=r!  for some positive integer r is

  1. A

    2014 

  2. B

    2013

  3. C

    1

  4. D

    2

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    Solution:

    We can rewrite the given expression as 

    kn2(n1)(n+1)(n2)(n+2)(n3)(n+3)…….(n+n1)(nn+1)=r!

    kn(1)(2)(n1)n(n+1)(n+2)(2n1)=r!kn(2n1)!=r!

     To convert L.H.S. to a factorial, we shall require

    k = 2 which will convert it into (2n)!

     

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