若数列{an}满足a1=1,a2=2且a(n+1)=an/a(n-1)(n≥2),则a2011的值

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若数列{an}满足a1=1,a2=2且a(n+1)=an/a(n-1)(n≥2),则a2011的值

若数列{an}满足a1=1,a2=2且a(n+1)=an/a(n-1)(n≥2),则a2011的值
若数列{an}满足a1=1,a2=2且a(n+1)=an/a(n-1)(n≥2),则a2011的值

若数列{an}满足a1=1,a2=2且a(n+1)=an/a(n-1)(n≥2),则a2011的值
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=1
a2=2
a3=2
a4=1
a5=1/2
a6=1/2
a7=1
a8=2
……
则a(2011)=a(335*6+1)=a(1)=1

由已知a(n+1)=an/a(n-1),得a(n+2)=a(n+1)/an
由上两式相乘得,a(n+2)=1/a(n-1)
则有a(n+5)=1/a(n+2)=1/(1/a(n-1)=a(n-1)
即a(n+6)=an,(n≥2)
所以有:a(2011)=a(335*6+1)=a(1)=1

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