1.已知数列{an}满足a1=1,a(n+1)(n+1为角标)=an+2,且前n项的和味Sn求(1)求数列{Sn/n}的前n项和Tn(2)求数列{1/Tn}的前n项和2.解不等式a(x-1)/(x-2)>2
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1.已知数列{an}满足a1=1,a(n+1)(n+1为角标)=an+2,且前n项的和味Sn求(1)求数列{Sn/n}的前n项和Tn(2)求数列{1/Tn}的前n项和2.解不等式a(x-1)/(x-2
1.已知数列{an}满足a1=1,a(n+1)(n+1为角标)=an+2,且前n项的和味Sn求(1)求数列{Sn/n}的前n项和Tn(2)求数列{1/Tn}的前n项和2.解不等式a(x-1)/(x-2)>2
1.已知数列{an}满足a1=1,a(n+1)(n+1为角标)=an+2,且前n项的和味Sn
求(1)求数列{Sn/n}的前n项和Tn
(2)求数列{1/Tn}的前n项和
2.解不等式a(x-1)/(x-2)>2
1.已知数列{an}满足a1=1,a(n+1)(n+1为角标)=an+2,且前n项的和味Sn求(1)求数列{Sn/n}的前n项和Tn(2)求数列{1/Tn}的前n项和2.解不等式a(x-1)/(x-2)>2
第一题:
1)
由递推关系 及 a1=1知:数列{an}是以1为首项2为公差的等差数列;
则:Sn=n^2……………………(就是n的平方了,下同);
则Tn=1+2+3+…+n=(1/2)*n*(n+1);
2)
1/Tn =2/[n*(n+1)]=2[(1/n)-(1/n+1)]…………(这是裂项相消);
设:Qn是数列{1/Tn}的前n项和;
则:Qn=2{[1-(1/2)]+[(1/2)-(1/3)]+…+[(1/n)-(1/n+1)]}=2-2/(n+1).
第二题:
原式等价于:ax^2-3ax+2(a-1)>0;
Δ=9a^2-4*a*2(a-1)=a^2+8a;
所以:
a
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