Question

若数列{an}满足：a（n+1）=1—1/an且a1=2,则a2011等于

Answer 1

a(n+3)=1-1/a(n+2)=1-a(n+1)/(a(n+1)-1)=-1/(a(n+1)-1)=an,因此{an}以3为周期,故a2011=a(670*3+1)=a1=2;