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Zene17
@Zene17
January 2020
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Simplifique as expressões:
a) (n!)/(n-1)!
b) (n+2)!/(n-1)!
c) [(n+1)!+n!]/2n!
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ProfRafael
Verified answer
A) (n!)/(n - 1)! = n.(n - 1)!/(n - 1)! = n
b) (n + 2)!/(n - 1)! = (n + 2)(n + 1).n.(n - 1)!/(n - 1)! = (n + 2)(n + 1).n = (n² + n + 2n + 2).n = (n² + 3n + 2).n = n³ + 3n² + 2n
c) [(n + 1)! + n!]/2n!
(n + 1)!/2n! + n!/2n! = (n + 1).n!/2n! + n!/2n! = (n + 1)/2 + 1/2 = (n + 1 + 1)/2 = (n + 2)/2 = n/2 + 1
Espero ter ajudado.
3 votes
Thanks 3
Zene17
Obrigado mais uma vez professor
Zene17
Só tem mais uns exercicios aqui vo postar , espero que vc me ajude.
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Verified answer
A) (n!)/(n - 1)! = n.(n - 1)!/(n - 1)! = nb) (n + 2)!/(n - 1)! = (n + 2)(n + 1).n.(n - 1)!/(n - 1)! = (n + 2)(n + 1).n = (n² + n + 2n + 2).n = (n² + 3n + 2).n = n³ + 3n² + 2n
c) [(n + 1)! + n!]/2n!
(n + 1)!/2n! + n!/2n! = (n + 1).n!/2n! + n!/2n! = (n + 1)/2 + 1/2 = (n + 1 + 1)/2 = (n + 2)/2 = n/2 + 1
Espero ter ajudado.