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24.47 - \(\frac{23}{24}\)+ 47 - 23
= 24.47 - 0.9583333333 + 47 - 23
= 23.51166667 + 47 - 23
= 70.51166667 - 23
= 47.51166667
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{24.47-23}{24+47-23}.\frac{3+\frac{3}{7}+\frac{3}{11}-\frac{3}{1001}+\frac{3}{13}}{\frac{9}{1001}-\frac{9}{13}+\frac{9}{7}+9}\)
\(A=\frac{1105}{48}.\frac{3.\left(1+\frac{1}{7}+\frac{1}{11}-\frac{1}{1001}+\frac{1}{13}\right)}{9.\left(\frac{1}{1001}-\frac{1}{11}+\frac{1}{7}+1\right)}\)
\(A=\frac{1105}{48}.\frac{3.\frac{1311}{1001}}{9.\frac{1054}{1001}}\)
\(A=\frac{1105}{48}.\frac{3933}{1001}:\frac{9468}{1001}\)
\(A=\frac{1105}{48}.\frac{437}{1052}\)
\(A\approx9,56\)
Chú ý : Dấu xấp xỉ \(\approx\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{24.47-23}{24+47-23}.\frac{3+\frac{3}{7}-\frac{3}{11}+\frac{3}{1001}-\frac{3}{13}}{\frac{9}{1001}-\frac{9}{13}+\frac{9}{7}-\frac{9}{11}+9}\)
\(A=\frac{1105}{28}.\)\(\frac{3+\frac{3}{7}-\frac{3}{11}+\frac{3}{1001}-\frac{3}{13}}{9+\frac{9}{7}-\frac{9}{11}+\frac{9}{1001}-\frac{9}{13}}\)
\(A=\frac{1105}{28}.\frac{3.\left(1+\frac{1}{7}-\frac{1}{11}+\frac{1}{1001}-\frac{1}{13}\right)}{9.\left(1+\frac{1}{7}-\frac{1}{11}+\frac{1}{1001}-\frac{1}{13}\right)}\)
\(A=\frac{1105}{28}.\frac{3}{9}\)
\(A=\frac{1105}{84}\)
b)\(M=\frac{1+2+2^2+2^3+...+2^{2012}}{2^{2014}-2}\)
Đặt \(A=1+2+2^2+2^3+...+2^{2012}\)
Suy ra \(2.A=2+2^2+2^3+2^4+...+2^{2013}\)
Khi đó \(2.A-A=2^{2013}-1\)hay \(A=2^{2013}-1\)
Do đó : \(M=\frac{A}{2^{2014}-2}=\frac{2^{2013}-1}{2^{2014}-2}=\frac{1}{2}\)
Vậy \(M=\frac{1}{2}\)
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