Question

O valor de n na expressão n! + (n -1)! / (n+1)! = 1/6

A) n = 5
B) n = 6
C) n= 7
D) n = 4
E) n= 3

Answer 1

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$\sf{\dfrac{n!+(n-1)!}{(n+1)!}=\dfrac{1}{6}}\\\sf{\dfrac{n\cdot(n-1)!+(n-1)! }{(n+1)\cdot n\cdot(n-1)!}=\dfrac{1}{6}}$

$\sf{\dfrac{\diagdown\!\!\!\!\!(n-1)!(n+1)}{(n+1)\cdot n\cdot\diagdown\!\!\!\!\!(n-1)!}=\dfrac{1}{6}}\\\sf{\dfrac{\diagdown\!\!\!\!\!(n+1)}{n\cdot\diagdown\! \!\!\!\!(n+1)}=\dfrac{1}{6}}\\\sf{\dfrac{1}{n}=\dfrac{1}{6}}$

$\huge\boxed{\boxed{\boxed{\boxed{\sf{n=6}}}}}$