Question

设数列xn满足xn>0,且limxn+1/xn=1/2

设数列{xn}满足xn+1=xn/2+1/xn,X0>0,n=0,1,2,3,...证明数列{xn}极限存在并求出其极限

Answer 1

简单计算一拍扰下即可胡贺磨，详情裤斗如图所示

Answer 2

注意灶慧纳到x(n+1)>=2√隐没碧帆(xn/2*1/xn)=√2,且x(n+1)-xn=1/xn-xn/2=(2-xn^2)/(2xn)