数列{an}满足a1=2,a(n+1)=(1+an)/(1-an) 求a1×a2×a3...a2011a2012的值
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数列{an}满足a1=2,a(n+1)=(1+an)/(1-an) 求a1×a2×a3...a2011a2012的值
数列{an}满足a1=2,a(n+1)=(1+an)/(1-an) 求a1×a2×a3...a2011a2012的值
数列{an}满足a1=2,a(n+1)=(1+an)/(1-an) 求a1×a2×a3...a2011a2012的值
a2=(1+a1)/(1-a1)=(1+2)/(1-2)=-3
a3=(1+a2)/(1-a2)=(1-3)/(1+3)=-1/2
a4=(1+a3)/(1-a3)=(1-1/2)/(1+1/2)=1/3
a5=(1+a4)/(1-a4)=(1+1/3)/(1-1/3)=2
…………
数列从第一项开始,按2,-3,-1/2,1/3循环,每4项循环一次.
(-3)(-1/2)(1/3)2=1
2012÷4=503,正好循环503次,每次循环4项的乘积都=1
a1a2a3...a2011a2012=1
先求出a,解a=-3/2,然后求an=(3n+5)/(3n+1),有规律可循先算出几个数,看能不能约。
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