Corrigé du 101 P. 46

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a. $\dfrac{(n+1)!}{n!} = \dfrac{(n+1) \times \cancel n \times \cancel{(n-1)}\cdots \times 1}{\cancel n\times \cancel{(n-1)}\cdots \times 1} = n+1.$

b. $\dfrac{n!}{n} = \dfrac{\cancel{n} \times (n-1)\times \cdots \times 1}{\cancel{n}} = (n-1)!.$

c. $\dfrac{(n+10)!}{(n+9)!} =\dfrac{(n+10)\times \cancel{(n+9)} \times \cancel{(n+8)} \times \cdots \times 1} {\cancel{(n+9)} \times \cancel{(n+8)} \times \cdots \times 1}$
$=n+10.$

d. $\dfrac{2n!}{n!} = 2\times \dfrac{n!}{n!} = 2\times 1 = 2$.

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