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Đặt: \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}+\frac{1}{256}\)
\(\Rightarrow A=\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^8}\)
\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^7}\)
\(\Rightarrow2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^2}\right)-\left(\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^8}\right)\)
\(\Rightarrow A=1-\frac{1}{2^7}\)
E= 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/128 + 1/256
2E = 2 ( 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/128 + 1/256 )
= 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128
=> E = 2E - E
= (1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128) - (1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 )
= 1 - 1/256
= 255/256
k nhá, thanks
![](https://rs.olm.vn/images/avt/0.png?1311)
S= 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256
2S= 2(1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256)
= 1+1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128
=>S = 2S-S =1+1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 -1/2 - 1/4 - 1/8 - 1/16 - 1/32 - 1/64 - 1/128 - 1/256
=1-1/256
=255/256
255/256
ht
và
NHỚ K CHO MIK NHA!!!!!!!!!!!!!!!!!
![](https://rs.olm.vn/images/avt/0.png?1311)
A = \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) + \(\dfrac{1}{64}\) + \(\dfrac{1}{128}\) + \(\dfrac{1}{256}\)
2A = 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) + \(\dfrac{1}{64}\) + \(\dfrac{1}{128}\)
2A - A = 1 - \(\dfrac{1}{256}\)
A = \(\dfrac{255}{256}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(E=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{256}\)
\(2\times E=1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{128}\)
\(2\times E-E=\left(1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{128}\right)-\left(\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{256}\right)\)
\(E=1-\dfrac{1}{256}\)
\(E=\dfrac{256}{256}-\dfrac{1}{256}\)
\(E=\dfrac{255}{256}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\text{Đặt }\)\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\)
\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)
\(\Rightarrow2A-A=1-\frac{1}{256}\)
\(=>A=\frac{255}{256}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + 1 / 32 + 1 / 64 + 1 / 128 = 127 / 128
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A= 1/2 + 1/4+ 1/8+ 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
A = 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 + 1/128 - 1/256 - 1/256 - 1/512
A = 1 - 1/512
A = 511/512
Chúc bạn học giỏi nha!
gọi biểu thức đó là A
A=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512
1/512+A=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/512
1/512+A=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/256
1/512+A=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128
1/512+A=1/2+1/4+1/8+1/16+1/32+1/64+1/64
1/512+A=1/2+1/4+1/8+1/16+1/32+1/32
1/512+A=1/2+1/4+1/8+1/16+1/16
1/512+A=1/2+1/4+1/8+1/8
1/512+A=1/2+1/4+1/4
1/512+A=1/2+1/2
1/512+A=1
A=1-1/512
A=511/512
chắc 100%
số số hạng của tổng là : \(\frac{2+256}{2}+1=130\)
A = (2 + 256) . 130 : 2 = 16770
Khoảng cách giữa các số hạng là: 4-2=2
Có số hạng là: (256-2) : 2+1=128 (số)
Tổng của dãy số là: (256+2) x 128 : 2= 16512
k mình nha