Question

simplifique:A)(n+2)!/(n+1)! B)(n-3)!/(n-2)! C)(n+1)!+n!/n! D)n!-(n-1)!/(n-1)!+(n-2)!

Answer 1

Oie, Td Bom?!

A)

= [(n + 2)!]/[(n + 1)!]

= [(n + 2) . (n + 1)!]/[(n + 1)!]

= n + 2

B)

= [(n - 3)!]/[(n - 2)!]

= [(n - 3)!]/[(n - 2) . (n - 3)!]

= 1/[n - 2]

C)

= [(n + 1)! + n!]/n!

= [(n + 1) . n! + n!]/n!

= [(n + 1 + 1) . n!]/n!

= [(n + 2) . n!]/n!

= n + 2

D)

= [n! - (n - 1)!]/[(n - 1)! + (n - 2)!]

= [n . (n - 1)! - (n - 1)!]/[(n - 1) . (n - 2)! + (n - 2)!]

= [(n - 1)! . (n - 1)]/[(n - 1 + 1). (n - 2)!]

= [(n - 1) . (n - 2)! . (n - 1)]/[n . (n - 2)!]

= [(n - 1) . (n - 1)]/n

= [(n - 1)²]/n

= [n² - 2n . 1 + 1²]/n

= [n² - 2n + 1]/n

Att. Makaveli1996