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Math Help - use the definition to prove the following :

  1. #1
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    use the definition to prove the following :

     \frac {n^3}{n!} \to 0
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  2. #2
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    Hi there, I would expand this quoient out and see what happens

     \frac {n^3}{n!} = \frac{n \times n \times n}{n\times (n-1) \times (n-2)\times (n-3)\times \dots}= \frac{n \times n }{ (n-1) \times (n-2)\times (n-3)\times \dots} = \dots
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  3. #3
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    Hi!
    I would check that n^3 = n(n-1)(n-2) + 3n(n-1) +n.
    This gives
    \frac{n^3}{n!}= \frac{ n(n-1)(n-2)}{n!} +\frac{ 3n(n-1)}{n!} + \frac{n}{n!} = \frac{1}{(n-3)!} +\frac{3}{(n-2)!} +\frac{1}{(n-1)!},
    each summand clearly goes to zero.
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