uh đúng rồi

kết quả sai rồi phải là \(\frac{1023}{1024}\)

làm vậy cũng dc nhưng kết quả phải là \(\frac{1023}{1024}\) hén

\(A=\left(1-\dfrac{1}{2}\right)+\left(1-\dfrac{1}{4}\right)+\left(1-\dfrac{1}{8}\right)+.......................+\left(1-\dfrac{1}{1024}\right)\)

\(\Leftrightarrow A=\dfrac{1}{2}+\dfrac{3}{4}+\dfrac{7}{8}+..................+\dfrac{1023}{1024}\)

\(\Leftrightarrow A=\dfrac{1}{2}+\dfrac{3}{2^2}+\dfrac{7}{2^3}+...............+\dfrac{1023}{2^{10}}\)

\(\Leftrightarrow2A=1+\dfrac{3}{2}+\dfrac{7}{2^2}+...............+\dfrac{1023}{2^9}\)

\(\Leftrightarrow2A-A=\left(1+\dfrac{3}{2}+\dfrac{7}{2^2}+............+\dfrac{1023}{2^9}\right)-\left(\dfrac{1}{2}+\dfrac{3}{2^2}+\dfrac{7}{2^3}+...............+\dfrac{1023}{2^{10}}\right)\)\(\Leftrightarrow A=1+\left(\dfrac{3}{2}-\dfrac{1}{2}\right)+\left(\dfrac{7}{2^2}-\dfrac{3}{2^2}\right)+.................+\left(\dfrac{1023}{2^9}-\dfrac{511}{2^9}\right)-\dfrac{1023}{2^{10}}\)\(\Leftrightarrow A=\left(1+1+...+1\right)-\dfrac{1023}{2^{10}}\)

\(\Leftrightarrow A=9-\dfrac{1023}{2^{10}}\)

Mk lm tắt nha

Hk bik có đúng hk nữa

A= 1/2-1/12024

.... Tự tính kết quả nha

gọi A = 1/2+1/4+1/8+......+1/1024                                                                                                                                                                          2 x A = 1 + 1/2 + 1/4+......+1/1024                                                                                                                                                                         2 x A - A = (1+1/2+1/4 +....+1/512) - (1/2+1/4+1/8+.....1/1024)                                                                                                                      A= 1-1/1024 = 1023/1024   vậy A= 1023/1024

trả lời 

A =1023/1024

chúc bn 

hc tốt

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

A x 2 = 1 - 1/1024 + A

A x 2 - A = 1 - 1/1024

A = 1 - 1/1024 

A = 1023 /1024

Đặt tổng trên là A. Ta có

A x 2 = 1+ 1/2+1/4+1/8+ 1/16+1/32+ 1/64+ 1/128 + 1/256 + 1/512

Ax2 - A = 1+ 1/2+1/4+1/8 +1/16 + 1/32 +1/64+ 1/128 + 1/256+ 1/512 - ( 1/2 + 1/4 +1/8+1/16+1/32+1/64 + 1/128+ 1/256 + 1/512+ 1/1024)

A = 1+ 1/2 +1/4+1/8+1/16+1/32+1/64+1/128+1/256 + 1/512 - 1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256-1/512- 1/1024

A = 1 - 1/ 1024 = 1023/1024

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

A = [ 1 - 1/2 ] + [ 1/2 - 1/4 ] + [ 1/4 - 1/8 ] + .... + [ 1/256 - 1/512 ] + [ 1/512 - 1/2024 ]

Ta xóa các phân số trùng lặp đi , ta được :

A = 1 - 1/2024

A = 2023/2024

Thấy đúng thì ủng hộ nha !!!

= \(\frac{1023}{1024}\)nha ban 

k minh nha 

A = 1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 + ..... + 1/256 - 1/512 + 1/512 - 1/1024

A = 1 - 1/1024

A = 1023/1024

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

A = \(\frac{1}{2}\)+ \(\frac{1}{4}\)+ \(\frac{1}{8}\)+ .....+\(\frac{1}{512}\)+\(\frac{1}{1024}\)

Gấp biểu thức A lên 2 lần ta có :

A x 2 = (\(\frac{1}{2}\)+ \(\frac{1}{4}\)+ \(\frac{1}{8}\)+ .....+ \(\frac{1}{512}\)+ \(\frac{1}{1024}\)) x 2

A x 2 = \(\frac{1x2}{2}\)+ \(\frac{1x2}{4}\)+ \(\frac{1x2}{8}\)+.....+ \(\frac{1x2}{512}\)+ \(\frac{1x2}{1024}\)

A x 2 = \(1\)+ \(\frac{1}{2}\)+\(\frac{1}{4}\)+....+\(\frac{1}{256}\)+\(\frac{1}{512}\)

A x (2 - 1)= 1 + \(\frac{1}{2}\)+\(\frac{1}{4}\)+ ....+ \(\frac{1}{256}\)+ \(\frac{1}{512}\)-  \(\frac{1}{2}\)-\(\frac{1}{4}\)-\(\frac{1}{8}\)-......- \(\frac{1}{512}\)-\(\frac{1}{1024}\)

A = \(1\)- \(\frac{1}{1024}\)

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

A = \(\frac{1023}{1024}\)

Ta có: A=1/2 + 1/4 + 1/8 +...+ 1/512 + 1/1024                                                                                                                                                            2A= 1+ 1/2 + 1/4+...+1/256+1/512                                                                                                                                                                  2A - A=(1+1/2+1/4+...+1/256+1/512) - ( 1/2+1/4+1/8+...+1/512+1/1024)                                                                                                                 suy ra A= 1 - 1/1024= 1023/1024                   . Vậy A = 1023/1024.        nhớ chọn câu trả lời của mình nha!

\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....+\frac{1}{512}+\frac{1}{1024}\)

Đặt tổng trên là A , ta có :

\(A\times2=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{512}+\frac{1}{1024}\right)\)

\(A\times2=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{512}+\frac{1}{1024}\right)\times2\)

\(A\times2=\frac{1}{2}\times2+\frac{1}{4}\times2+\frac{1}{8}\times2+...+\frac{1}{512}\times2+\frac{1}{1024}\times2\)

\(A\times2=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{512}+\frac{1}{1024}\)

\(A\times2-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{512}+\frac{1}{1024}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{512}+\frac{1}{1024}\right)\)

\(A=\left(1-\frac{1}{1024}\right)+\left(\frac{1}{2}-\frac{1}{2}\right)+\left(\frac{1}{4}-\frac{1}{4}\right)+\left(\frac{1}{8}-\frac{1}{8}\right)+....+\left(\frac{1}{256}-\frac{1}{256}\right)+\left(\frac{1}{1024}-\frac{1}{1024}\right)\)

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

Nguyễn Linh Chi : Mong cô check bài này cho em ạ !!

Đặt S = 1/2 + 1/4 + 1/8 + 1/16 + ... 
==> 2S = 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... 
2S = 1 + S 
==> S = 1 

Ta có 2xA=1+1/2+...+1/512

Do đó: A=2xA-A=1-1/1024=1023/1024.