已知数列{an}满足a1=2,an+1【n+1是下标】=1+an/1-an（n属于N+）,则a1·a2·a3...·a2003=

题目

已知数列{an}满足a1=2,an+1【n+1是下标】=1+an/1-an（n属于N+）,则a1·a2·a3...·a2003=

答案

an+1=(1+an)/(1-an)∵a1=2∴ a2=(1+2)/(1-2)=-3∴ a3=(1-3)/(1+3)=-1/2∴ a4=(1-1/2)/(1+1/2)=1/3∴ a5=(1+1/3)/(1-1/3)=2∴ {an}是周期数列,周期为4连续四项的和为2*(-3)*(-1/2)*(1/3)=12003=4*500+3∴ a1·a2·a3....