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A=1/2+1/4+1/8.....+1/256+1/512
2A=1+1/2+1/4+1/8...1/256
A=(1+1/2+1/4+1/8...1/256)-(1/2+1/4+1/8.....+1/256+1/512)
A=1-1/512
A=511/512
511/512
![](https://rs.olm.vn/images/avt/0.png?1311)
Các số là :
(512 + 1 ) : 1 + 1 = 512 (so )
Tổng trên là :
(512 - 1 ) .512 : 2= 130816
Vậy tổng trên bằng 130816
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^9}\\ 2A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^8}\\ 2A-A=\left(1+\dfrac{1}{2}+...+\dfrac{1}{2^8}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}\right)\\ A=1-\dfrac{1}{2^9}=\dfrac{511}{512}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}+\frac{1}{512}\)
\(A\cdot2=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\)
\(A\cdot2-A=1-\frac{1}{512}\)
\(A=\frac{511}{512}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :1/2+1/4=1-1/4=3/4
1/2+1/4+1/8=1-1/8=7/8
Tương tự
Vậy 1/2+1/4+1/8+1/16+....+1/256+1/512
=1-1/512
=511/512
![](https://rs.olm.vn/images/avt/0.png?1311)
1/2 + 1/4+ 1/8+ 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
= 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
= 1 – 1/512
= 511/512 .
1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 + 1/1024
Ta có :
1/512 = 1×2 / 512×2 = 2/1024
1/256 = 1×4 / 256×4 = 4/1024
1/128 = 1×8 / 128×8 = 8/1024
1/64 = 1×16 / 64×16 = 16/1024
1/32 = 1×32 / 32×32 = 32/1024
1/16 = 1×64 / 16×64 = 64/1024
1/8 = 1×128 / 8×128 = 128/1024
1/4 = 1×256 / 4×256 = 256/1024
1/2 = 1×512 / 2×512 = 512/1024
___________________________
=>
1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 + 1/1024
= 512/1024 + 256/1024 + 128/1024 + 64/1024 + 32/1024 + 16/1024 + 8/1024 + 4/1024 + 2/1024 + 1/1024
= (512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1) / 1024
= 1023/1024
![](https://rs.olm.vn/images/avt/0.png?1311)
Cho \(a=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+....+\frac{1}{512}\)
Nên \(2a=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\)
\(2a-a=a=1-\frac{1}{512}=\frac{511}{512}\)
Vậy \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{512}=\frac{511}{512}\)
Bài này dễ.
Giải:
Đặt tổng trên là A, ta có:
\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{256}+\frac{1}{512}\)
\(2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{512}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\right)\)
\(A=1-\frac{1}{1024}\)
\(A=\frac{1023}{1024}\)
Chúc bạn học tốt.
1 + 2 + 4 + 8 + .......753........ + 256 + 512 = 1.536
Tk mk nha
~~~chúc bn hok tốt~~~
^_^