Define the binomial coefficient by  for r = 0, 1, 2,n.(a)   Show that   for r = 1, 2, 3,n....

Define the binomial coefficient by

  for r = 0, 1, 2,n.

(a)   Show that

   for r = 1, 2, 3,n.

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(b)  Use part (a) and mathematical induction to prove the binomial theorem: