Answered

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(n+3)!-(n+2)!/
(n + 1)!+n!
ifadesinin eşiti aşağıdakilerden hangisidir?
A) n2 +3n+2 B) n2+3n C) n2+n


D) n+2
E) n +1

Sagot :

Şeymarans

(n+3)! = (n+3).(n+2)!

(n+3)!-(n+2)! = (n+3).(n+2)!-(n+2)!

Ortak paranteze al: (n+2)!(n+3-1)

→ (n+2).(n+2)!

(n+1)! = (n+1).n!

(n+1)!+n! = (n+1).n!+n!

Ortak paranteze al: n!(n+1+1)

→ (n+2).n!

[tex] \frac{(n + 3)! - (n + 2)!}{(n + 1)! + n!} = \frac{(n + 2).(n + 2)!}{(n + 2).n!} [/tex]= [tex] \frac{(n + 2)!}{n!} [/tex]

(n+2)! = (n+2).(n+1).n!

→ (n+2).(n+1).n! / n! = (n+2).(n+1)

Cevap: n²+3n+2

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