数列{an}满足a1=3/5,an=2-1/(a(n-1)) (n>=2),数列{bn}=1/
问题描述:
数列{an}满足a1=3/5,an=2-1/(a(n-1)) (n>=2),数列{bn}=1/
数列{an}满足a1=3/5,an=2-1/(a(n-1)) (n>=2),数列{bn}=1/(an-1)
(1)求证:数列{bn}是等差数列
(2)求数列{an}的通项
答
(1)an=2-1/a(n-1),(an-1)=1-1/a(n-1)1/(an-1)=1/[1-1/a(n-1)]=[a(n-1)/[a(n-1)-1)]=1/[a(n-1)-1]+1.∵bn=1/(an-1)∴bn-b(n-1)=1,b1=1/(a1-1)=1/(3/5-1)=-5/2.∴数列{b}是首项为-5/2、公差为1的等差数列.(2)bn=-5/2...太给力了,你的回答完美解决了我的问题!