Question

prove that n(n+1)(n+2) is divisible by 6

Answer 1

n(n+1)(n+2) = 6d

P(1) = 1(1+2)(2+3)

  = 2X3 = 6

P(k) = k(k+1)(k+2) = 6d  ........(i)

P(k+1) = (k+1)(k+2)(k+3)

  = 6d/k(k+3)  (from (i))

  =6d(k+3/k)

hence proved
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