Resolva as equações:
a) (n+2)! - n!/5! = 330
S= {6}
Ola Lucas
( n + 2)! - n!/5! = 330
/n + 2)*(n + 1)*n! - n! = 330*5!
n² + 3n + 2 - 1)*n! = 330*5!
(n² + 3n + 1)*n! = 330*5!
n! = 330*5!/(n² + 3n + 1)
n! = (11*30*5!)(/n² + 3n + 1) = (11*5*6*5!)/(n² + 3n + 1) = (55*6!)/(n² + 3n + 1)
se n = 6
n² + 3n + 1 = 36 + 18 + 1 = 55
n! = 55*6!/55 = 6!
n = 6
pronto
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Ola Lucas
( n + 2)! - n!/5! = 330
/n + 2)*(n + 1)*n! - n! = 330*5!
n² + 3n + 2 - 1)*n! = 330*5!
(n² + 3n + 1)*n! = 330*5!
n! = 330*5!/(n² + 3n + 1)
n! = (11*30*5!)(/n² + 3n + 1) = (11*5*6*5!)/(n² + 3n + 1) = (55*6!)/(n² + 3n + 1)
se n = 6
n² + 3n + 1 = 36 + 18 + 1 = 55
n! = 55*6!/55 = 6!
n = 6
pronto