【高考】若数列{an}满足,a1=1,且a(n+1)=an/(1+an),设数列{bn}的前n项和为Sn,且Sn=2-bn,求{bn/an}的前...

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【高考】若数列{an}满足,a1=1,且a(n+1)=an/(1+an),设数列{bn}的前n项和为Sn,且Sn=2-bn,求{bn/an}的前...
【高考】若数列{an}满足,a1=1,且a(n+1)=an/(1+an),设数列{bn}的前n项和为Sn,且Sn=2-bn,求{bn/an}的前n项和Tn

1/a(n+1)=1/an+11/a1=11/an=n,an=1/nsn=2-bn,b1=1sn=2-bn,s(n+1)=2-b(n+1)b(n+1)=(1/2)*bnbn=(1/2)^(n-1)Tn=1+2*(1/2)^1+...+n*(1/2)^(n-1)2Tn=2+2+...+n*(1/2)^(n-2)Tn=4-(2+n)*(1/2)^(n-1)