lim (n→∞) [(an^2+bn+c)/(2n+5)]=3,求a,b

题目

lim (n→∞) [(an^2+bn+c)/(2n+5)]=3,求a,b
写出过程．

答案

首先a＝0,否则极限不存在.
又lim (n→∞)[(an^2+bn+c)/(2n+5)]
＝lim (n→∞)[(bn+c)/(2n+5)]
＝lim (n→∞)[(b+c/n)/(2+5/n)]
＝b/2=3
∴b＝6.
∴a＝0,b＝6.