高二数学题（等差数列）
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(1)
an = 2(Sn)^2/(2Sn-1)
Sn -S(n-1) = 2(Sn)^2/(2Sn-1)
2(Sn)^2- Sn -2Sn.S(n-1)+ S(n-1) =2(Sn)^2
- Sn -2Sn.S(n-1)+ S(n-1) =0
S(n-1)-Sn = 2Sn.S(n-1)
1/Sn - 1/S(n-1) =2
=>{1/Sn} 是等差数列
(2)
1/Sn - 1/S1 =2(n-1)
1/Sn = 2n-1
Sn = 1/(2n-1)
an = Sn -S(n-1)
= 1/(2n-1) -1/(2n+1)
an =1 ; n=1
= 1/(2n-1) -1/(2n+1) ; n>=2
an = 2(Sn)^2/(2Sn-1)
Sn -S(n-1) = 2(Sn)^2/(2Sn-1)
2(Sn)^2- Sn -2Sn.S(n-1)+ S(n-1) =2(Sn)^2
- Sn -2Sn.S(n-1)+ S(n-1) =0
S(n-1)-Sn = 2Sn.S(n-1)
1/Sn - 1/S(n-1) =2
=>{1/Sn} 是等差数列
(2)
1/Sn - 1/S1 =2(n-1)
1/Sn = 2n-1
Sn = 1/(2n-1)
an = Sn -S(n-1)
= 1/(2n-1) -1/(2n+1)
an =1 ; n=1
= 1/(2n-1) -1/(2n+1) ; n>=2
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