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2014-09-03T18:53:42-03:00
a) \dfrac{3!.5!}{4!.6!} = \dfrac{\not3!.\not5!}{4.\not3!.6.\not5!}= \boxed{\dfrac{1}{24}}
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b) \dfrac{(n+1)!}{(n+2)!} = \dfrac{(n+1)!}{(n+2).(n+1)!}=\boxed{\dfrac{1}{(n+2)}}
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c) \dfrac{(n+3)!}{(n-2)!}\cdot \dfrac{(n-1)!}{(n+2)!}=\dfrac{(n+3)!.(n-1)!}{(n-2)!.(n+2)!} = \\ \\ \\ =\dfrac{(n+3).(n+2)!.(n-1).(n-2)!}{(n-2)!.(n+2)!}=(n+3)(n-1) = n^2-n+3n-3 \\ \\ \\ \boxed{=n^2+2n-3}
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