= 2047/2048 nhé

2017/2048

= 2047/2048

Ta co: 2S=2+1+1/2+1/4+...+1/2048

          2S-S=2+1+1/2+1/4+...+1/2048-1-1/2-1/4-...-1/2048-1/4096

         \(\Rightarrow\)S=2-1/4096 =8191/4096

cảm ơn bạn nha

4095/4096

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

\(\Rightarrow A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{11}}\)

\(\Rightarrow2A=2\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{11}}\right)\)

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

\(\Rightarrow2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{10}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{11}}\right)\)

\(\Rightarrow A=1-\frac{1}{2^{11}}=\frac{2^{11}-1}{2^{11}}=\frac{2047}{2048}\)
 

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

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

\(A=1-\frac{1}{2048}=\frac{2047}{2048}\)

\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+....+\frac{1}{2048}\)

\(=\left(1+\frac{1}{2}+\frac{1}{4}+....+\frac{1}{2048}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2048}\right)\)

\(=1-\frac{1}{2048}\)

\(=\frac{2047}{2048}\)

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

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

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

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

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

Đặt A = 1 + 2 + 4 + ... + 2048

A = 1 + 2 + 2² + ... + 2¹¹

2A = 2 + 2² + 2³ + ... + 2¹²

2A - A = ( 2 + 2² + 2³ + ... + 2¹² ) - ( 1 + 2 + 2² + ... + 2¹¹ )

A = 2¹² - 1

4095

HỌC TỐT

bn ơi sao cách này giống cấp 2 z