ko bít

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

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

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

\(\Rightarrow A=1-\frac{1}{1024}=\frac{1023}{1024}\)

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

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

=> \(2A-A=1-\frac{1}{1024}\)

=> \(A=\frac{1023}{1024}\)

\(B=2+2^2+2^3+...+2^{10}\)

\(2B=2^2+2^3+...+2^{11}\)

\(2B-B=\left(2^2+2^3+...+2^{11}\right)-\left(2+2^2+...+2^{10}\right)\)

\(B=2^{11}-2\)

a)

Từ 1 đến 23 gồm có (29-1) : 2 + 1 = 15 số

15 số gồm có 7.5 cặp

Mà từng cặp số có tổng bằng 30 (tính từng cặp số ở hai đầu)

Vậy S = 30 * 7.5

          = 225

          =

bạn có thể trình bày theo cách của tiểu học đuọc ko

tính như bth thôi ráng lên bạn nhá

99/32

\(y x 4/9 - 5/8 = 1/2 : 2/3\)

\(y x 4/9 - 5/8 = 3/4\)

\(y x 4/9 = 3/4 + 5/8\)

\(y x 4/9 = 11/8\)

\(y = 11/8 : 4/9\)

\(y = 99/32\)

Đặt \(A=-1-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-...-\frac{1}{2014}\)

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

\(-A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\)

\(\Rightarrow-2A=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)

\(\Rightarrow-2A-\left(-A\right)=\left(2+1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^9}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{10}}\right)\)

\(-A=2-\frac{1}{2^{10}}\)

\(\Rightarrow A=\frac{1}{2^{10}}-2\)

Đặt: \(A=1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+...+\dfrac{1}{512}+\dfrac{1}{1024}\)

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

\(\Rightarrow2A=2+1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{512}\)

\(\Rightarrow2A-A=\left(3+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{512}\right)-\left(1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{1024}\right)\)

\(\Rightarrow A=\left(\dfrac{1}{2}-\dfrac{1}{2}\right)+\left(\dfrac{1}{4}-\dfrac{1}{4}\right)+...+\left(3-1-\dfrac{1}{1024}\right)\)

\(\Rightarrow A=2-\dfrac{1}{1024}\)

\(\Rightarrow A=\dfrac{2047}{1024}\)

 1+(1)/(2)+(1)/(4)+(1)/(8)+...+(1)/(512)+(1)/(1024)

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