若数列{An}中满足a1=1,a2=2,且an=an-1/an-2,则a2010等于?

Question

若数列{An}中满足a1=1,a2=2,且an=an-1/an-2,则a2010等于?

Answer 1

∵a1＝1,a2＝2且an=an-1/an-2,∴a1=1,a2=2 ,a3＝2 ,a4＝1 ,a5＝½ ,a6＝½ ,a7＝1 ,a8＝2 ,a9＝2 ,a10＝1 .可以看出有周期,且周期为6 .2010÷6＝335,没有余数,∴a2010＝a6＝½