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Math Help - 2 questions on factorial

  1. #1
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    2 questions on factorial

    (1) Why is (r+1)r!=(r+1)!

    (2)This is commonly asked : why is 0! =1 ??
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  2. #2
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    Quote Originally Posted by mathaddict View Post
    (1) Why is (r+1)r!=(r+1)!

    (2)This is commonly asked : why is 0! =1 ??
     (r+1)r! = (r+1) \times r(r-1)(r-2)(r-3)\times ...\times 1

     (r+1)! = (r+1)(r+1-1)(r+1-2)(r+1-3)\times ...\times 1 = (r+1)(r)(r-1)(r-2)\times ...\times 1

    See how they are identical?

    Also. We know that  n!= n(n-1)(n-2)(n-3)...1 . This can be written  n! = n(n-1)!

    So, let's look at n = 1, knowing that  1! = 1

     1! = 1(1-1)!

     1 = 1(0)!

     1 = 0! .
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