已知数列{an}的前n项和Sn,且Sn+1/2an=1
问题描述：
已知数列{an}的前n项和Sn,且Sn+1/2an=1
设bn=log3（1-Sn+1）,求适合方程1/b1b2+1/b2b3+``````+1/bnbn+1=25/51的n的值
答
Sn+(1/2)an=1n=1,a1= 2/3Sn+(1/2)an=1Sn+(1/2)[Sn-S(n-1)]=1(3/2)Sn = (1/2)S(n-1) +1Sn = (1/3)S(n-1) + (2/3)Sn - 1 = (1/3)(S(n-1) - 1){Sn - 1} 是等比数列,q=1/3Sn - 1 = (1/3)^(n-1) .[S1 - 1]=-1/3^nSn = 1- ...