Đặt \(A=1+2+2^2+2^3+...+2^{2012}\)
Có \(2A=2+2^2+2^3+2^4+...+2^{2013}\)
\(2A-A=\left(2+2^2+2^3+2^4+...+2^{2013}\right)-\left(1+2+2^2+2^3+...+2^{2012}\right)\)
\(A=2^{2013}-1\)
Vậy \(M=\frac{2^{2013}-1}{2.\left(2^{2012}-1\right)}=\frac{1}{2}\)
\(M=\frac{1}{2}\)
Tính giá trị của biểu thức sau bằng cách hợp lý:
B = \(\frac{\frac{2012}{2}+\frac{2012}{3}+\frac{2014}{4}+...+\frac{2012}{2013}}{\frac{2012}{1}+\frac{2011}{2}+\frac{2010}{3}+...+\frac{1}{1012}}\)
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M=\(\frac{2014}{1}+\frac{2013}{2}+\frac{2012}{3}+...+\frac{2}{2013}+\frac{1}{2014}\)
\(B=\frac{1-3}{1\cdot3}+\frac{2-4}{2\cdot4}+\frac{3-5}{3\cdot5}+\frac{4-6}{4\cdot6}+............+\frac{2011-2013}{2011.2013}+\frac{2012-2014}{2012\cdot2014}-\frac{2013+2014}{2013\cdot2014}\)
Tìm x biết
\(\left(\frac{1}{2}+\frac{1}{3}+....+\frac{1}{2014}+\frac{1}{2015}\right).x=\frac{2014}{1}+\frac{2013}{2}+\frac{2012}{3}+...+\frac{2}{2013}+\frac{1}{2014}\)
tìm x biết :(\(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2014}.x=\frac{2013}{1}+\frac{2012}{2}+....+\frac{2}{2012}+\frac{1}{2013}\)
\(\frac{1+\frac{1}{2}+\frac{1}{3}+....\frac{1}{2012}}{\frac{2013}{1}+\frac{2014}{2}+\frac{2015}{3}....\frac{4024}{2012}-2012}\)
tính nhanh cả nhà ơi
\(\frac{1+2+2^2+2^3+....+2^{2012}}{2^{2014}-2}\)
Cho \(A=\frac{1}{2014}+\frac{2}{2013}+\frac{3}{2012}+..+\frac{2013}{2}+\frac{2014}{1}\)
\(B=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}+\frac{1}{2015}\)
Tính \(\frac{A}{B}\)
Tính nhanh
A = \(\left(\frac{2014}{2}+\frac{2014}{3}+\frac{2014}{4}+...+\frac{2014}{2015}\right):\left(\frac{2014}{1}+\frac{2013}{2}+\frac{2012}{3}+...+\frac{1}{2014}\right)\)
