Question

Calcule o valor da expressão envolvendo fatoriais de números naturais: 12! / 7!

Answer 1

Fórmula:

$\Large\bm{} \dfrac{n!}{\left(n + 1\right)!}$

Sabendo da fórmula vamos lá:

$\Large\bm{} \dfrac{12!}{7!} \\\\\Large\bm{} \dfrac{12\cdot11\cdot10\cdot9\cdot8\cdot7!}{7!}\\\\ \Large\bm{}\dfrac{12\cdot11\cdot10\cdot9\cdot8\cdot\cancel{7!}}{\cancel{7!}} \\\\\\\Large\bm{}12 \cdot11\cdot10 \cdot9\cdot8 \\ \Large\bm{}120\cdot11\cdot9\cdot8 \\ \Large\bm{}1320\cdot9\cdot8 \\ \Large\bm{}11880\cdot8 \\ \Large\bm{}95040$

Solução:

$\Large\begin{gathered} \begin{gathered}\large \overline{ \boxed{\boxed{ \begin{array}{r}\mathsf{ 95040 }\end{array}}}} \end{gathered}  \end{gathered}$

Forma alternativa:

$\Large\begin{gathered} \begin{gathered}\large \overline{ \boxed{\boxed{ \begin{array}{r}\mathsf{ 9,504 \cdot {10}^{4} }\end{array}}}} \end{gathered}  \end{gathered}$

$\bm\Large\begin{gathered} \begin{gathered}\large \overline{ \boxed{\boxed{ \begin{array}{r}\mathsf{\red{Bons~Estudos} }\end{array}}}} \end{gathered}  \end{gathered}$