Question

resolva as fatoriais: A) 7!/10! B) (k+2)!/(k+1)! C) 5! + 4!/3!

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Answer 1

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$\tt a)~\sf\dfrac{7!}{10!}=\dfrac{\diagdown\!\!\!\!\!\!7!}{10\cdot9\cdot8\cdot\diagdown\!\!\!\!\!\!7!}=\dfrac{1}{720}\checkmark\\\tt b)~\sf\dfrac{(k+2)!}{(k+1)!}=\dfrac{(k+2)\cdot\diagup\!\!\!(k\diagup\!\!\!\!\!\1+\diagup\!\!\!1)!}{\diagup\!\!\!(k\diagup\!\!\!\!+\diagup\!\!\!1)!}=k+2\checkmark\\\tt c)~\sf\dfrac{5!+4!}{3!}=\dfrac{5\cdot4\cdot3!+4\cdot3!}{3!}=\dfrac{\diagdown\!\!\!\!\!\!3!\cdot(5\cdot4+4)}{\diagdown\!\!\!\!\!3!}=20+4=24\checkmark$