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1-2+3-4+5-6+...+2011-2012
=2012-2011+...+6-5+4-3+2-1
=(2012-2001)+...+(6-5)+(4-3)+(2-1)
=1+1+1+...+1+1(có 1006 số 1)
=1x60
=60
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{2}{3}+\frac{1}{3}\left(\frac{-4}{9}+\frac{5}{6}\right)\div\frac{7}{12}\)
\(=\frac{2}{3}+\frac{1}{3}\left(\frac{-4}{9}+\frac{5}{6}\right)\times\frac{12}{7}\)
\(=\frac{2}{3}+\frac{4}{7}\left(\frac{-4}{9}+\frac{5}{6}\right)\)
\(=\frac{2}{3}+\frac{4}{7}\left(\frac{-8}{18}+\frac{15}{18}\right)\)
\(=\frac{2}{3}+\frac{4}{7}.\frac{-7}{18}\)
\(=\frac{6}{9}+\frac{-2}{9}\)
\(=\frac{4}{9}\)
\(\frac{298}{719}\div\left(\frac{1}{4}+\frac{1}{12}-\frac{1}{3}\right)-\frac{2011}{2012}\)
\(=\frac{298}{719}\div\left(\frac{3}{12}+\frac{1}{12}-\frac{4}{12}\right)-\frac{2011}{2012}\)
\(=\frac{298}{719}\div0-\frac{2011}{2012}\)
Vậy biểu thức đại số này không xác định
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Bài 2:1-2+3-4+...+2011-2012
=1+2+3+4+...+2011+2012-2(2+4+6+...+2012)
=2025078-2(1012036)
=2025078-2024072
=1006
Học giỏi!
![](https://rs.olm.vn/images/avt/0.png?1311)
c)\(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{2012}}\)
\(2A=2\left(1+\frac{1}{2}+\frac{1}{2^2}+.....+\frac{1}{2^{2012}}\right)\)
\(2A=2+1+\frac{1}{2^2}+\frac{1}{2^3}+.....+\frac{1}{2^{2011}}\)
\(2A-A=\left(2+1+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....\frac{1}{2^{2012}}\right)\)
\(A=2-\frac{1}{2^{2012}}\)
1/
A=1/1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100
A=1/1-1/100
Vì 1/100>0
-->1/1-1/100<1
-->A<1