设a>0,数列{an}满足：a0>0,a(n+1)=1/2(an+a/an),n=1,2,3.,求n趋于∞时lim an

题目

设a>0,数列{an}满足：a0>0,a(n+1)=1/2(an+a/an),n=1,2,3.,求n趋于∞时lim an

答案

极限是根号a
（1）a(n+1)=1/2(an+a/an)>=根号(an*a/an)=根号(a)
(2)a(n+1)-a(n)=1/2(a/an-an)=(a-an^2)/(2an)=根号(a)