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7 tháng 5 2017

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 : \(6-\frac{3}{2^9}\)

7 tháng 5 2017

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 :

\(B=2-\frac{1}{2^9}\)

\(\Rightarrow A=3.\left(2-\frac{1}{2^9}\right)\)

\(\Rightarrow A=6-\frac{3}{2^9}\)

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 \(S=\frac{3069}{512}\)

\(S=3+\frac{3}{2}+\frac{3}{2^2}+.....+\frac{3}{2^9}\)

\(\Rightarrow\frac{1}{2}S=\frac{3}{2}+\frac{3}{2^2}+\frac{3}{2^3}+.....+\frac{3}{2^{10}}\)

\(\Rightarrow S-\frac{1}{2}S=\left(3+\frac{3}{2}+\frac{3}{2^2}+....+\frac{3}{3^9}\right)-\left(\frac{3}{2}+\frac{3}{2^2}+.....+\frac{3}{2^{10}}\right)\)

\(\Rightarrow\frac{S}{2}=3-\frac{3}{2^{10}}\)

\(\Rightarrow S=\left(3-\frac{3}{2^{10}}\right).2\)\(=6-\frac{3}{2^9}\)

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 \(S=3\left(1-\frac{1}{2^9}\right)=3\left(1-\frac{1}{512}\right)=3-\frac{3}{512}=\frac{1533}{512}\)

27 tháng 3 2019

\(S=3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\)

\(\Leftrightarrow2S=6+3+\frac{3}{2}+...+\frac{3}{2^8}\)

\(\Leftrightarrow2S-S=6-\frac{3}{2^9}\)

\(\Leftrightarrow S=6-\frac{3}{2^9}\)

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 \(A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)

=> \(2A=2+1+\frac{1}{2}+\frac{1}{2^8}\)

=> \(A=2A-A=2-\frac{1}{2^9}\)

=> \(S=3A=3\left(2-\frac{1}{2^9}\right)=6-\frac{3}{2^9}\)

\(S=3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\)

\(S=\frac{3}{1}.2+\frac{3}{2}.3+....+\frac{3}{8}.9\)

\(S=3-\frac{3}{9}\)

\(S=\frac{27}{9}+\frac{3}{9}\)

\(S=\frac{30}{9}\)
\(<=>S=3\frac{1}{3}\)

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

11 tháng 5 2016

\(S=3+\frac{3}{2}+\frac{3}{2^2}+....+\frac{3}{2^9}\)

=>\(2S=6+3+\frac{3}{2}+.....+\frac{3}{2^8}\)

=>\(2S-S=\left(6+3+\frac{3}{2}+....+\frac{3}{2^8}\right)-\left(3+\frac{3}{2}+\frac{3}{2^2}+....+\frac{3}{2^9}\right)\)

=>\(S=6-\frac{3}{2^9}=\frac{3069}{512}\)

11 tháng 5 2016

\(2S=2\left(3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\right)\)

\(2S=6+3+\frac{3}{2}+...+\frac{3}{2^8}\)

\(2S-S=\left(6+3+\frac{3}{2}+...+\frac{3}{2^8}\right)-\left(3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\right)\)

\(S=6-\frac{3}{2^9}\)