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X x (1/2+1/4+1/8+1/16+1/32+1/64+1/128) = 127/128
X x 127/128 = 127/128
X = 127/128 : 127/128
X = 1
![](https://rs.olm.vn/images/avt/0.png?1311)
b: A=1/3+1/9+...+1/3^10
=>3A=1+1/3+...+1/3^9
=>A*2=1-1/3^10=(3^10-1)/3^10
=>A=(3^10-1)/(2*3^10)
c: C=3/2+3/8+3/32+3/128+3/512
=>4C=6+3/2+...+3/128
=>3C=6-3/512
=>C=1023/512
d: A=1/2+...+1/256
=>2A=1+1/2+...+1/128
=>A=1-1/256=255/256
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C= \(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}+\dfrac{1}{128}\)
2C = \(1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}\)
2C-C = \(1-\dfrac{1}{128}\)
C= \(\dfrac{127}{128}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1/2+1/4+1/8+1/16+1/32+1/64+1/128
=1/1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32+1/32-1/64+1/64-1/128
=1/1-1/128
=127/128
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Gọi biểu thức trên là A ta có
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)
=> \(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
=> \(A=2A-A\)\(=1-\frac{1}{128}\)
Vậy \(A=1-\frac{1}{128}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Gọi tổng này là A
<=> 2A = 1 + 1/2 + 1/4 + ... + 1/64
=> 2A - A = ( 1 + 1/2 + 1/4 + ... + 1/64 ) - ( 1/2 + 1/4 + 1/8 + ... + 1/128 )
A = 1 - 1/128
A = 127/128
Ủng hộ ae ơiii
![](https://rs.olm.vn/images/avt/0.png?1311)
1/2+1/4+1/8+1/16+1/32+1/64+1/128
=1/1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32+1/32-1/64+1/64-1/128
=1/1-1/28
=128/128-1/128
=127/128
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-\frac{1}{32}-\frac{1}{64}-\frac{1}{128}\)
\(=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\right)-2\times\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\right)\)
\(=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-\frac{1}{32}-\frac{1}{64}\)
\(=\frac{1}{128}\)< 1
còn 1 cách nữa mk lm nhưng ko chắc nên hỏi
1/2-(1/4+1/8+1/32+1/64+1/128)
=1/2-(1/2-1/4+1/4-1/8+1/8-1/32+1/32-1/64+1/64-1/128)
=1/2-(1/2-1/128)
=1/2-63/128
=1/128