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3A = 3.(3 + 32 + 33 + ... + 32004)
3A = 32 + 33 + 34 + ... + 32005
2A = 3A - A = (32 + 33 + .... + 32005) - (3 + 32 + 33 + ... + 32004)
2A = 22005 - 3
=> A = \(\frac{2^{2005}-3}{2}\)
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A = 3 + 32 + 33 + ... + 32004
3A = 32 + 33 + 34 + ... + 32005
3A - A = 32 + 33 + 34 + ... + 32005 - 3 - 32 - 33 - ... - 32004
2A = 32005 - 3
A = (32005 - 3) : 2
3A = 3(3+32+...+32004)
3A = 32+33+...+32005
3A-A= 32005 + 3
2A = 32005 +3
A = 32005 + 3 / 2
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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
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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
A= 3+32+33+34+....+32004
3A = 32+33+34+....+32004+32005
3A - A = (32+33+34+....+32004+32005) + (3+32+33+34+....+32004)
A = (32005 + 3) : 2
Học tốt nhé ~!!!!!
\(A=3+3^2+3^3+3^4+...+3^{2004}\)
\(\Rightarrow\) \(3A=3^2+3^3+3^4+3^5+...+3^{2004}+3^{2005}\)
\(\Rightarrow\) \(2A=3^{2005}-3\)
\(\Rightarrow\) \(A=\frac{3^{2005}-3}{2}\)