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4 tháng 3 2016

A = 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/512 + 1/1024

A x 2 = 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/512

A x 2 - A = 1 + 1/2 - 1/2+ 1/4 -1/4 + 1/8 -1/8 + 1/16 -1/16 + ... + 1/512 - 1/512 - 1/1024

A = 1 - 1/1024

A = 1023/1024

4 tháng 3 2016

la 1023/1024 ban nha

24 tháng 10 2023

Đặt $A=\dfrac12+\dfrac14+\dfrac18+\dfrac{1}{16}+...+\dfrac{1}{1024}$

$A=\dfrac12+\dfrac{1}{2^2}+\dfrac{1}{2^3}+\dfrac{1}{2^4}+...+\dfrac{1}{2^{10}}$

$\dfrac12\cdot A=\dfrac{1}{2^2}+\dfrac{1}{2^3}+\dfrac{1}{2^4}+\dfrac{1}{2^5}+...+\dfrac{1}{2^{11}}$

$A-\dfrac{1}{2}A=(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+\dfrac{1}{2^4}+...+\dfrac{1}{2^{10}})-(\dfrac{1}{2^2}+\dfrac{1}{2^3}+\dfrac{1}{2^4}+\dfrac{1}{2^5}+...+\dfrac{1}{2^{11}})$

$\dfrac{1}{2}A=\dfrac{1}{2}-\dfrac{1}{2^{11}}$

$\dfrac{1}{2}A=\dfrac{1}{2}\cdot(1-\dfrac{1}{2^{10}})$

$\Rightarrow A=1-\dfrac{1}{2^{10}}$

Vậy: ...

$Toru$

13 tháng 3 2017

A = 1/2+1/4+...+1/2048

2A= 1+ 1/2+ 1/4+...+1/1024

2A-A= ( 1+ 1/2+...+1/1024 ) -  (1/2+1/4+...+2048)

A= 1- 1/2048

A= 2047/2048

26 tháng 7 2016

\(M=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{502}+\frac{1}{1024}\)

\(M\cdot2=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{502}+\frac{1}{1024}\right)\cdot2\)

\(M\cdot2=\frac{1}{2}\cdot2+\frac{1}{4}\cdot2+\frac{1}{8}\cdot2+\frac{1}{16}\cdot2+...+\frac{1}{502}\cdot2+\frac{1}{1024}\cdot2\)

\(M\cdot2=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{504}\)

\(M\cdot2-M=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{502}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{502}+\frac{1}{1024}\right)\)

\(M=1-\frac{1}{1024}\)

\(M=\frac{1023}{1024}\)

15 tháng 6

= (y+y+y+y+...+y)+(1/2+1/4+1/8+1/16+...+1/1024)=1

          y x 512         +                1023/1024                     =1

         y x 512          =1-1023/1024

         y x 512          =1/1024

          y                    =1/1024:512

         y=1/524,288

15 tháng 6

mk trình bày hơi lệch xíu

12 tháng 8 2016

Đặt A = 1/2 + 1/4 + 1/8 + ... + 1/1024

2A = 1 + 1/2 + 1/4 + ... + 1/512

2A - A = (1 + 1/2 + 1/4 + ... + 1/512) - (1/2 + 1/4 + 1/8 + ... + 1/1024)

A = 1 - 1/1024

A = 1023/1024

12 tháng 8 2016

mk ko hieu cho lam

19 tháng 6 2019

B x 2 = 1 - ( 1/2 + 1/4 + 1/8 + 1/16 + ..... + 1/512 + 1/1024 ) - 1/1024

B x 2 = 1 - 1/1024 + A

B x 2 - B = 1 - 1/1024

B = 1 - 1/1024

B = 1023 /1024

19 tháng 6 2019

làm lại bài kia sai 1 chỗ 

\(B=1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}-...+\frac{1}{1024}\)

\(\Rightarrow Bx2=1-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\right)-\frac{1}{1024}\)

\(\Rightarrow Bx2=1-\frac{1}{1024}+B\)

\(\Rightarrow Bx2-B=1-\frac{1}{1024}\)

\(\Rightarrow B=\frac{1023}{1024}\)

17 tháng 2 2022

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14 tháng 9

b-1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256

7 tháng 6 2018

Đặt \(A=1-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-..-\frac{1}{2048}\)

\(\Rightarrow A=1-\left(1-\frac{1}{2}\right)-\left(\frac{1}{2}-\frac{1}{4}\right)-..-\left(\frac{1}{1024}-\frac{1}{2048}\right)\)

\(\Rightarrow A=1-1+\frac{1}{2}-\frac{1}{2}+\frac{1}{4}-..-\frac{1}{1024}+\frac{1}{2018}\)

\(\Rightarrow A+\frac{1}{2018}\)

7 tháng 6 2018

1-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256-1/512-1/1024-1/2048 =0.00048828125