Question

Simplifique as equações:

Answer 1

$a) \dfrac{n! (n+1)!}{n!} = \dfrac{\not n! (n+1)!}{\not n!} = \boxed{ (n+1)! } \\ \\ \\ \\ b) \dfrac{(n+2)! +(n+1)(n-1)! }{(n+1)(n-1)!} = \\ \\ \\ \dfrac{(n+2)(n+1)(n)(n-1)! +(n+1)(n-1)! }{(n+1)(n-1)!} = \\ \\ \\ \dfrac{(n-1)! * \left[(n+2)(n+1)(n) +(n+1) \right] }{(n+1)(n-1)!} = \\ \\ \\ \dfrac{ \left[(n+2)(n+1)(n) +(n+1) \right] }{(n+1)} = \\ \\ \\ \dfrac{(n+1) \left[(n+2)(n) +1 \right] }{(n+1)} = (n+1)*n+1= \boxed{n^1+n+1}$



Até outra vez!!!!