已知数列{an}中,a1=1,a2=2,ana(n+1)a(n+2)=an+a(n+1)+a(n+2),ana(n+1)≠1,则a2009=?

问题描述:

已知数列{an}中,a1=1,a2=2,ana(n+1)a(n+2)=an+a(n+1)+a(n+2),ana(n+1)≠1,则a2009=?
=2

∵ana(n+1)a(n+2)=an+a(n+1)+a(n+2)∴a(n+2)=(an+a(n+1))/(ana(n+1)-1)∵a1=1,a2=2∴a3=(a1+a2)/(a1a2-1)=3a4=(a2+a3)/(a2a3-1)=1a5=(a3+a4)/(a3a4-1)=2a6=(a4+a5)/(a4a5-1)=3a7=(a5+a6)/(a5a6-...