Fatorial

por **aninhapmello25** » Seg Abr 16, 2018 11:59

Alguém pode me ajudar a resolver esses exercícios de fatorial ?

por **Gebe** » Seg Abr 16, 2018 17:45

4a)
$\\ \frac{\left[\left(p+1 \right)! \right]^2}{p!}\\ \\ \frac{\left(p+1 \right)!\left(p+1 \right)!}{p!}\\ \\ \frac{\left(p+1 \right)!\left(p+1 \right)\left(p+1-1 \right)!}{p!}\\ \\ \frac{\left(p+1 \right)!\left(p+1 \right)\left(p \right)!}{p!}\\ \\ (p+1)(p+1)!\;\;ou\;\;(p+1)^2p!$

4b)
$\\ \frac{m!(m-p)!p!}{(m+2)!(m-p-1)!(p-1)!}\\ \\ \\ \frac{\left[m! \right]\;\left[(m-p)(m-p-1)! \right]\;\left[p(p-1)! \right]}{\left[(m+2)(m+1)m! \right]\;\left[(m-p-1)! \right]\;\left[(p-1)! \right]}\\ \\ \\ \frac{\left[(m-p)\right]\;\left[p \right]}{\left[(m+2)(m+1)\right]}\\ \\ \\ \frac{(m-p)p}{(m+2)(m+1)}\\$

4c)
$\\ \frac{\left(n! \right)^2(n+1)!\;n!}{(n+2)!\;n!}\\ \\ \\ \frac{\left(n! \right)^2\;(n+1)!\;n!}{(n+2)(n+1)!\;n!}\\ \\ \\ \frac{\left(n! \right)^2}{(n+2)}\;\;ou\;\;\frac{n!\;n!}{(n+2)}$

5a)
$\\ n(n-1)(n-2)\\ \\ n(n-1)(n-2)\;*\;\frac{1}{1} \\ \\ n(n-1)(n-2)\;*\;\frac{n-3}{n-3}\\ \\ \\ n(n-1)(n-2)\;*\;\frac{\left( n-3 \right)!}{\left( n-3 \right)!}\\ \\ \\ \frac{n(n-1)(n-2)\left( n-3 \right)!}{\left( n-3 \right)!} \\ \\ \frac{n!}{(n-3)!}$

5b)
$\\ (n^2-1)=(n+1)(n-1)\;\;\;e\;\;\;(n^2-4)=(n+2)(n-2)\\ \\ n(n^2-1)(n^2-4)\\ \\ n\;\;(n+1)(n-1)\;\;(n+2)(n-2)\\ \\ reorganizando\\ \\ (n+2)\;(n+1)\;n\;(n-1)\;(n-2)\\ \\ (n+2)\;(n+1)\;n\;(n-1)\;(n-2)\;\;*\frac{(n-3)!}{(n-3)!}\\ \\ \\ \frac{(n+2)\;(n+1)\;n\;(n-1)\;(n-2)\;(n-3)!}{(n-3)!}\\ \\ \frac{(n+2)!}{(n-3)!}\\$

Espero ter ajudado, se ficarem duvidas mande msg. Bons estudos.

Fatorial

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