Question

Simplifique:

A) 10!/7!
B) 7!/8!
C) (n+1)!/(n+2)!
D) (n+2)!/n!

Answer 1

Olá



A)

$\displaystyle\mathsf{ \frac{10!}{7!}~=~ \frac{10\cdot 9\cdot 8\cdot \diagup\!\!\!\!7!}{\diagup\!\!\!\!7!} ~=~10\cdot 9\cdot 8~=~\boxed{720 }}$




B)

$\displaystyle\mathsf{ \frac{7!}{8!}~=~ \frac{\diagup\!\!\!\!7!}{8\cdot \diagup\!\!\!\!7! }~=~ \boxed{\frac{1}{8} }}$




C)

$\displaystyle\mathsf{ \frac{(n+1)!}{(n+2)!} ~=~ \frac{(\diagup\!\!\!n+\diagup\!\!\!\!1)!}{(n+2)\cdot (\diagup\!\!\!\!n+\diagup\!\!\!1)!}~=~ \boxed{\mathsf{\frac{1}{n+2} }}}$




D)

$\displaystyle\mathsf{ \frac{(n+2)!}{n!}~=~ \frac{(n+2)(n+1)\diagup\!\!\!\!n!}{\diagup\!\!\!\!\!n!} ~=~\boxed{\mathsf{(n+2)(n+1)}}}$