已知数列{an}满足a1=2,an+1=- 1/(an+1),则a2009

问题描述:

已知数列{an}满足a1=2,an+1=- 1/(an+1),则a2009

a2=-1/(1+2)=-1/3
a3=-1/(-1/3+1)=-3/2
a4=-1/(-3/2+1)=2=a1
所以是三个一循环
2009÷3余数=2
所以a2009=a2=-1/3