已知数列{an}满足a1=2,an+1【n+1是下标】=1+an/1-an(n属于N+),则a1·a2·a3...·a2
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已知数列{an}满足a1=2,an+1【n+1是下标】=1+an/1-an(n属于N+),则a1·a2·a3...·a2003=
/>an+1=(1+an)/(1-an)
∵a1=2
∴ a2=(1+2)/(1-2)=-3
∴ a3=(1-3)/(1+3)=-1/2
∴ a4=(1-1/2)/(1+1/2)=1/3
∴ a5=(1+1/3)/(1-1/3)=2
∴ {an}是周期数列,
周期为4
连续四项的和为2*(-3)*(-1/2)*(1/3)=1
2003=4*500+3
∴ a1·a2·a3...·a2003=
=a1·a2·a3.(a4..·a2003)
=a1.a2.a3
=2*(-3)*(-1/2)
=3
∵a1=2
∴ a2=(1+2)/(1-2)=-3
∴ a3=(1-3)/(1+3)=-1/2
∴ a4=(1-1/2)/(1+1/2)=1/3
∴ a5=(1+1/3)/(1-1/3)=2
∴ {an}是周期数列,
周期为4
连续四项的和为2*(-3)*(-1/2)*(1/3)=1
2003=4*500+3
∴ a1·a2·a3...·a2003=
=a1·a2·a3.(a4..·a2003)
=a1.a2.a3
=2*(-3)*(-1/2)
=3
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