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\(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}\)\(=\dfrac{16}{32}+\dfrac{8}{32}+\dfrac{4}{32}+\dfrac{2}{32}+\dfrac{1}{32}=\dfrac{31}{32}\)
1/2+1/4+1/8+1/16+1/32
=3/4+1/8+1/16+1/32
=7/8+1/16+1/32
=15/16+1/32
=31/32
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^5}\)
\(2A=1+\frac{1}{2}+...+\frac{1}{2^4}\)
\(2A-A=A=1-\frac{1}{2^5}=1-\frac{1}{32}=\frac{31}{32}\)
đặt tổng là A
=>\(A=\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^5}\)
=>\(2A=1+\frac{1}{2}+...+\frac{1}{2^4}\)
=>\(2A-A=\left(1+\frac{1}{2}+...+\frac{1}{2^4}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+.....+\frac{1}{2^5}\right)=1-\frac{1}{2^5}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-\frac{1}{32}\)
\(=1-\frac{1}{32}=\frac{31}{32}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A=\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)
\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
\(2A-A=1-\frac{1}{128}\)
\(A=\frac{127}{128}\)
\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}=\frac{127}{128}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A=1/2+1/4+1/8+1/16+1/32+...+1/2048+1/4096
\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{12}}\)
\(2A=2\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{12}}\right)\)
\(2A=1+\frac{1}{2}+...+\frac{1}{2^{11}}\)
\(2A-A=\left(1+\frac{1}{2}+...+\frac{1}{2^{11}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{12}}\right)\)
\(A=1-\frac{1}{2^{12}}\)
đặt A=1/2 + 1/4 + 1/8 + 1/16 + 1/32
=>2A=1+1/2+1/4+1/8+1/16
=>2A-A=A=1-1/32=31/32