Question

数列极限的题目已知lim(n趋向无穷大)(5n-根号(an^2-bn+c))=2,求a,b的值

Answer 1

lim(5n)-lim((an^2-bn+c)^0.5)=2

lim(5n-2)=lim((an^2-bn+c)^0.5)

根据lim的唯一性,可知

5n-2=(an^2-bn+c)^0.5

即：(5n-2)^2=an^2-bn+c

于是得：a=25,b=10