Question

Simplifique a expressão

(n + 2)! + (n + 1)! / (n + 1)!

me ajuda pfv

Answer 1

$\large\boxed{\begin{array}{l}\underline{\rm D~\!\!efinic_{\!\!,}\tilde ao\,de\,fatorial}\\\tt Seja\,n\,um\,n\acute umero\inteiro\,n\tilde ao\,negativo(n\in\mathbb{N}).\\\tt D~\!\!efinimos\,fatorial\,de\,n(e\,indicamos\,por\,n!)\\\tt por\,meio\,da\,relac_{\!\!,}\tilde ao\\\sf n!=\begin{cases}\sf 1,~se~n=0\,ou\,n=1\\\sf n\cdot (n-1)\cdot (n-2)\cdot...3\cdot2\cdot1\,~se~n\geqslant2\end{cases}\end{array}}$

$\large\boxed{\begin{array}{l}\sf (n+2)!=(n+2)\cdot(n+2-1)!\longrightarrow (n+2)\cdot (n+1)!\\\\\sf\dfrac{(n+2)!+(n+1)!}{(n+1)!}\\\\\sf \dfrac{(n+2)\cdot(n+1)!+(n+1)!}{(n+1)!}\\\\\sf\dfrac{\diagup\!\!\!\!\!\!(n+\diagup\!\!\!\!1)!\cdot(n+2+1)}{\diagup\!\!\!\!\!\!(n+\diagup\!\!\!\!\!\!1)!}=n+3\end{array}}$