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

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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

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
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

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)=3
a4=(a2+a3)/(a2a3-1)=1
a5=(a3+a4)/(a3a4-1)=2
a6=(a4+a5)/(a4a5-1)=3
a7=(a5+a6)/(a5a6-1)=1
.
即当n=3k(k是整数)时,a(3k)=3
当n=3k+1(k是整数)时,a(3k+1)=1
当n=3k+2(k是整数)时,a(3k+2)=2
∵ 2009=3*669+2
∴ a2009=2