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Ta có: S = 30 + 32 + 34 + 36 + … + 32002 (1)
Nhân cả hai vế của (1) cho 9, ta được:
9S = 32(30 + 32 + 34 + 36 + … + 32002)
9S = 32 + 34 + 36 + 38 + … + 32004 (2)
Lấy (2) - (1), ta được:
9S - S = (32 + 34 + 36 + 38 + … + 32004) - (30 + 32 + 34 + 36 + … + 32002)
8S = 32004 - 30
8S = 32004 - 1
Khi đó:
8S - 32004 - 1 = 32004 - 1 - 32004 - 1
8S - 32004 - 1 = -2
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Đề sai nhé: phải là 8S-..+1 nhé
Có: \(3^2.S=3^2+3^4+3^6+...+3^{2004}\)
\(\Rightarrow3^2S-S=3^{2004}-1\)\(\Leftrightarrow8S=3^{2004}-1\Leftrightarrow8S-3^{2004}+1=0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
S= 3^0+3^2+3^4+...+3^2002
<=> 9S=3^2+3^4+3^6+...+3^2004
<=>9S-S=(3^2+3^4+3^6+...+3^2004)-(3^0+3^2+3^4+...+3^2002)
<=>8S=3^2004-1
Khi đó: 8S-3^2004-1=3^2004-1-3^2004-1=0-1-1=-2
![](https://rs.olm.vn/images/avt/0.png?1311)
S=\(3^0+3^2+3^4+...+3^{2002}\)
\(3^2\cdot S=3^2+3^4+3^6+...+3^{2004}\)
9S-S=\(\left(3^2+3^4+3^6+...+3^{2004}\right)-\left(3^0+3^2+3^4+...+3^{2002}\right)\)
8S=\(3^{2004}-3^0\)
8S-\(3^{2004}-1\)=\(3^{2004}-1-3^{2004}-1\)=-2
![](https://rs.olm.vn/images/avt/0.png?1311)
S=3^0+3^2+3^4+..+3^2002
=1+3^2+3^4+...+3^2002
3^2S=3^2+3^4+3^6+...+3^2004
9S-S=3^2+3^4+3^6+...+3^2004-1-3^2-3^4-...-3^2002
8S=3^2004-1
S=(3^2004-1):8
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
\(S=3^0+3^2+3^4+...+3^{2002}\)
\(3^2S=3^2+3^4+...+3^{2004}\)
\(9S-S=\left(3^2+3^4+3^6+...+3^{2004}\right)-\left(3^0+3^2+3^4+...+3^{2002}\right)\)
\(8S=3^{2004}-3^0\)
\(8S-3^{2004}=-1\)
\(8S-3^{2004}-1=-2\)
Vậy \(8S-3^{2004}-1=-2\)