数列{an}满足a1=2,an+1=(1+an)/(1-an) ,n+1,n为下标,n属于N*,则a1*a2*a3*.*a2010的值?
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数列{an}满足a1=2,an+1=(1+an)/(1-an),n+1,n为下标,n属于N*,则a1*a2*a3*.*a2010的值?数列{an}满足a1=2,an+1=(1+an)/(1-an),n
数列{an}满足a1=2,an+1=(1+an)/(1-an) ,n+1,n为下标,n属于N*,则a1*a2*a3*.*a2010的值?
数列{an}满足a1=2,an+1=(1+an)/(1-an) ,n+1,n为下标,n属于N*,则a1*a2*a3*.*a2010的值?
数列{an}满足a1=2,an+1=(1+an)/(1-an) ,n+1,n为下标,n属于N*,则a1*a2*a3*.*a2010的值?
a1=2,an+1=(1+an)/(1-an) ,
可以依次计算出数列的前几项:
a1=2,a2=-3,a3=-1/2,a4=1/3,a5=2,a6=-2,……
可以发现数列是以4为周期的数列.
a1*a2*a3*a4=1.
2010=4*502+2.
则a1*a2*a3*.*a2010=( a1*a2*a3*a4)^502 *( a1*a2)
=1*(2*(-3))=-6.
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