若数列{an}满足a1=1,a2=2且a(n+1)=an/a(n-1)(n≥2),则a2011的值
问题描述：
若数列{an}满足a1=1,a2=2且a(n+1)=an/a(n-1)(n≥2),则a2011的值
答
由已知a(n+1)=an/a(n-1)则a(n+2)=a(n+1)/an两式相乘得,a(n+2)=1/a(n-1)则a(n+5)=1/a(n+2)=a(n-1)即a(n+6)=an由已知a1=1a2=2a3=2a4=1a5=1/2a6=1/2a7=1a8=2……则a(2011)=a(335*6+1)=a(1)=1