Ta có :
\(S=1-\frac{1}{2}+\frac{1}{4}-...+\frac{1}{1024}\)
\(S=1-\frac{1}{2}+\frac{1}{2^2}-...+\frac{1}{2^{10}}\)
\(\frac{1}{2}S=\frac{1}{2}-\frac{1}{2^2}+\frac{1}{2^3}-...+\frac{1}{2^{11}}\)
\(S+\frac{1}{2}S=\left(1-\frac{1}{2}+\frac{1}{2^2}-...+\frac{1}{2^{10}}\right)+\left(\frac{1}{2}-\frac{1}{2^2}+\frac{1}{2^3}-...+\frac{1}{2^{11}}\right)\)
\(\frac{3}{2}S=1-\frac{1}{2^{11}}\)
\(S=\frac{1-\frac{1}{2^{11}}}{\frac{3}{2}}\)
\(S=\frac{2-\frac{1}{2^{10}}}{3}\)
\(S=\frac{\frac{2^{11}-1}{2^{10}}}{3}\)
Vậy \(S=\frac{\frac{2^{11}-1}{2^{10}}}{3}\)
Chúc bạn học tốt ~
Ta có:
2S = 2.(1-1/2+1/4-1/8+1/16-...+1/1024)
2S = 2/2-1+1/2-1/4+1/8-...+1/512
2S+S = ( 2/2-1+1/2-1/4+1/8-...+1/512)+(1-1/2+1/4-1/8+1/16-...+1/1024)
3S = 2 + 1/1024
3S = 2048/1024+1/1024
3S = 2049/1024
S = 2049/1024 : 3
S = 2049/1024.1/3
S = 683/1024
Cho mình sửa lại chỗ kia nhé :
\(\frac{3}{2}S=1+\frac{1}{2^{11}}\)
\(S=\frac{1+\frac{1}{2^{11}}}{\frac{3}{2}}\)
\(S=\frac{2+\frac{1}{2^{10}}}{3}\)
\(S=\frac{\frac{2^{11}+1}{2^{10}}}{3}\)
\(S=\frac{\frac{2048+1}{1024}}{3}\)
\(S=\frac{\frac{2049}{1024}}{3}\)
\(S=\frac{2049}{1024}.\frac{1}{3}\)
\(S=\frac{683}{1024}\)
Vậy \(\frac{683}{1024}\)
Sửa lại giúp mk nhé sorry bạn >.<
