Oblicz granice Xxx: Oblicz granice Lim n! − (n−1) ! + (n−2) ! / −2n! + 2(n−2)! Hmm... nie wiem czy da się jakoś inaczej zapisać n! ? (n−2)(n−1)n ?

Student: n! = (n−2)! * (n−1) * n

Student: licznik: n! − (n−1)! + (n−2)! = (n−2)!*(n−1)*n − (n−2)!*(n−1) + (n−2)! = = (n−2)![(n−1)*n − (n−1) + 1] = (n−2)![n²−n−n+1+1] = (n−2)![n²−2n+2] mianownik: −2n! + 2(n−2)! = −2(n−2)!*(n−1)*n + 2(n−2)! = (n−2)![−2(n−1)*n+2] = = (n−2)![−2(n²−n) + 2] = (n−2)![−2n²+2n+2] zatem

licznik		(n−2)![n2−2n+2]		n2−2n+2
	=		=
mianownik		(n−2)![−2n2+2n+2]		−2n2+2n+2

z tego juz policzysz granice.

Basia:

n!−(n−1)!+(n−2)!
	=
−2n! + 2(n−2)!

(n−2)![(n−1)*n −(n−1)+1]
	=
(n−2)![−2(n−1)*n+2]

n2−n −n+1+1
	=
−2(n2−n)+2

n2−2n+2		1		1
	→		= −
−2n2−2n+2		−2		2