Tính tổng:\(3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\)
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PT
1
29 tháng 7 2018
\(2S=6+3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^8}\)
\(=9+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^8}\)
\(\Rightarrow2S-S=\left(9+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^8}\right)-\left(3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\right)\)
\(\Rightarrow S=6-\frac{3}{2^9}=6-\frac{3}{512}=\frac{3069}{512}\)
NT
1
7 tháng 5 2017
\(S=3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\)
\(2S=6+3+\frac{3}{2}+...+\frac{3}{2^8}\)
\(2S-S=\left(6+3+\frac{3}{2}+...+\frac{3}{2^8}\right)-\left(3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\right)\)
\(S=6-\frac{3}{2^9}\)
\(S=6-\frac{3}{512}\)
\(S=\frac{3069}{512}\)
Vậy \(S=\frac{3069}{512}\)
V
3
5 tháng 5 2017
\(S=3+\frac{3}{2}+\frac{3}{2^2}+.....+\frac{3}{2^9}\)
\(\Rightarrow\frac{1}{2}S=\frac{3}{2}+\frac{3}{2^2}+\frac{3}{2^3}+.....+\frac{3}{2^{10}}\)
\(\Rightarrow S-\frac{1}{2}S=\left(3+\frac{3}{2}+\frac{3}{2^2}+....+\frac{3}{3^9}\right)-\left(\frac{3}{2}+\frac{3}{2^2}+.....+\frac{3}{2^{10}}\right)\)
\(\Rightarrow\frac{S}{2}=3-\frac{3}{2^{10}}\)
\(\Rightarrow S=\left(3-\frac{3}{2^{10}}\right).2\)\(=6-\frac{3}{2^9}\)
S
5 tháng 5 2017
\(S=3\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^9}\right)\)
Đặt \(A=\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)
\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^8}\)
\(\Rightarrow2A-A=A=1-\frac{1}{2^9}\)
Do đó \(S=3\left(1-\frac{1}{2^9}\right)=3\left(1-\frac{1}{512}\right)=3-\frac{3}{512}=\frac{1533}{512}\)
A2
1
KN
27 tháng 3 2019
\(S=3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\)
\(\Leftrightarrow2S=6+3+\frac{3}{2}+...+\frac{3}{2^8}\)
\(\Leftrightarrow2S-S=6-\frac{3}{2^9}\)
\(\Leftrightarrow S=6-\frac{3}{2^9}\)
LP
1
KK
1
HT
30 tháng 4 2017
\(S=3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\)
=> \(S=3\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)\)
Đặt \(A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)
=> \(2A=2+1+\frac{1}{2}+\frac{1}{2^8}\)
=> \(A=2A-A=2-\frac{1}{2^9}\)
=> \(S=3A=3\left(2-\frac{1}{2^9}\right)=6-\frac{3}{2^9}\)
DV
2
8 tháng 5 2016
\(S=3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\)
\(S=\frac{3}{1}.2+\frac{3}{2}.3+....+\frac{3}{8}.9\)
\(S=3-\frac{3}{9}\)
\(S=\frac{27}{9}+\frac{3}{9}\)
\(S=\frac{30}{9}\)
\(<=>S=3\frac{1}{3}\)
8 tháng 5 2016
S=3+3/2+3/22+....+3/29
S=3/1.2+3/2.3+...+3/8.9
S=3-3/9=18/3-3/9=12/3
IW
8
HP
11 tháng 5 2016
\(S=3+\frac{3}{2}+\frac{3}{2^2}+....+\frac{3}{2^9}\)
=>\(2S=6+3+\frac{3}{2}+.....+\frac{3}{2^8}\)
=>\(2S-S=\left(6+3+\frac{3}{2}+....+\frac{3}{2^8}\right)-\left(3+\frac{3}{2}+\frac{3}{2^2}+....+\frac{3}{2^9}\right)\)
=>\(S=6-\frac{3}{2^9}=\frac{3069}{512}\)
TN
11 tháng 5 2016
\(2S=2\left(3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\right)\)
\(2S=6+3+\frac{3}{2}+...+\frac{3}{2^8}\)
\(2S-S=\left(6+3+\frac{3}{2}+...+\frac{3}{2^8}\right)-\left(3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\right)\)
\(S=6-\frac{3}{2^9}\)
Đặt \(A=3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\)
Nên \(2.A=6+3+\frac{3}{2}+....+\frac{3}{2^8}\)
Suy ra \(2.A-A=6-\frac{3}{2^9}\Rightarrow A=6-\frac{3}{2^9}\)
Vậy giá trị biểu thức là : \(6-\frac{3}{2^9}\)
đặt \(A=3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\)
\(A=3.\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)\)
đặt \(B=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)( 1 )
\(2B=2+1+\frac{1}{2}+...+\frac{1}{2^8}\)( 2 )
Lấy ( 2 ) - ( 1 ) ta được :
\(B=2-\frac{1}{2^9}\)
\(\Rightarrow A=3.\left(2-\frac{1}{2^9}\right)\)
\(\Rightarrow A=6-\frac{3}{2^9}\)