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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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3S=32+34+36+..+32003
3S-S=(32+34++.....+32003)-(3+32+...+32002)
2S=32003-3
S=(32003-3):2
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s = 3 ^0 + 3 ^ 2 + 3^ 4+ 3 ^6 +... + 3 ^2002
9S = 3 ^4 + 3^6 + 3 ^ 2004
9S - S= 3 ^ 2004 - 1
8S = 3^2004 - 1
S = 3 ^ 2004 - 1/8
k mk nha
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\(a,S=1+3^2+3^4+...+3^{2002}\)
\(3^2S=3^2+3^4+3^6+...+3^{2004}\)
\(8S=3^{2004}-1\)
\(S=\frac{3^{2004}-1}{8}\)
\(\text{a) }S=1+3^2+3^4+3^6+.....+3^{2000}+3^{2002}\)
\(3^2S=3^2+3^4+3^6+......+3^{2002}+3^{2004}\)
\(3^2S-S=\left(3^2+3^4+.....+3^{2004}\right)-\left(1+3^2+...+3^{2002}\right)\)
\(2^3S=2^{2004}-1\)
\(S=\frac{2^{2004}-1}{8}\)
\(S=1+3^2+3^4+3^6+....+3^{2002}\)
\(S=\left(1+3^2+3^4\right)+......+\left(3^{1998}+3^{2000}+3^{2002}\right)\)
\(S=1\left(1+3^2+3^4\right)+.....+3^{1998}\left(1+3^2+3^4\right)\)
\(S=1.91+....+3^{1998}.91\)
\(S=91\left(1+....+3^{1998}\right)\)
\(S=13.7\left(1+....+3^{1998}\right)⋮7\)
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a)Nhóm 4 số hạng liên tiếp từ số thứ 2
S=1+(2-3-4+5)+(6-7-8+9)+.....+(2002-2003-2004+2005)+2006=1+2006=2007
b)S=1-2+22-23+...+22002
=>2S=2-22+23-24+22003
=>S+2S=(1-2+22-23+...+22002)+(2-22+23-24+...+22003)
=>3S=1+22003
=>3S-22003\(=1+2^{2003}\)\(-2^{2002}\)\(=1\)
Trả lời :
Bạn Thắng Hoàng làm đúng rồi nha bạn !
Học tốt !
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