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A=1−3+5−7+...+2001−2003+2005S=1−3+5−7+...+2001−2003+2005
=(1−3)+(5−7)+...+(2001−2003)+2005=(1−3)+(5−7)+...+(2001−2003)+2005(Có 1002 cặp)
=(−2).1002+2005=(−2).1002+2005
=−2004+2005=−2004+2005
=1
a) \(\left(\frac{-3}{4}+\frac{2}{5}\right):\frac{3}{7}+\left(\frac{3}{5}+\frac{-1}{4}\right):\frac{3}{7}\)
= \(\left(-\frac{3}{4}+\frac{2}{5}+\frac{3}{5}+\frac{-1}{4}\right):\frac{3}{7}\)
= \(0:\frac{3}{7}\)
= \(0\)
b) \(\frac{2}{8}:\left(\frac{2}{9}-\frac{1}{18}\right)+\frac{7}{8}:\left(\frac{1}{36}-\frac{5}{12}\right)\)
= \(\frac{1}{4}:\frac{1}{6}+\frac{7}{8}:\frac{-7}{18}\)
=\(\frac{1}{4}.6+\frac{7}{8}.\frac{-18}{7}\)
= \(\frac{3}{2}-\frac{3}{4}\)
= \(\frac{3}{4}\)
\(\frac{1+2+3+4+5+6+7+8+9.0}{1+2+3+4+5+6+7+8+9.0}\)
= 1
( Vì tử và mẫu đều giống nhau )
a) \(\frac{-3}{7}+\frac{15}{26}-\left(\frac{2}{13}-\frac{3}{7}\right)=\frac{-3}{7}+\frac{15}{26}-\frac{2}{13}+\frac{3}{7}=\left(\frac{-3}{7}+\frac{3}{7}\right)+\left(\frac{15}{26}-\frac{2}{13}\right)\)
\(=\frac{15-4}{26}=\frac{11}{26}\)
c) \(\frac{-11}{23}.\frac{6}{7}+\frac{8}{7}.\frac{-11}{23}-\frac{1}{23}=\frac{-11}{23}.\left(\frac{6}{7}+\frac{8}{7}\right)-\frac{1}{23}\)
\(=\frac{-11}{23}.2-\frac{1}{23}=\frac{-22-1}{23}=\frac{-23}{23}=-1\)
câu a
\(\left(5\dfrac{7}{9}+2\dfrac{3}{11}\right)-\left(-1\dfrac{8}{11}+3\dfrac{7}{9}\right)\)
= \(5\dfrac{7}{9}+2\dfrac{3}{11}+1\dfrac{8}{11}-3\dfrac{7}{9}\)
= \(\left(5\dfrac{7}{9}-3\dfrac{7}{9}\right)+\left(2\dfrac{3}{11}+1\dfrac{8}{11}\right)\)
= \(2+3\dfrac{11}{11}\)
= \(2+3+1\)
= \(6\)
câu b
\(\left(2\dfrac{7}{19}-3\dfrac{8}{9}\right)-\left(1\dfrac{7}{19}-2\dfrac{1}{9}\right)\)
= \(2\dfrac{7}{19}-3\dfrac{8}{9}-1\dfrac{7}{19}+2\dfrac{1}{9}\)
= \(\left(2\dfrac{7}{19}-1\dfrac{7}{19}\right)-\left(3\dfrac{8}{9}-2\dfrac{1}{9}\right)\)
= \(1-1\dfrac{7}{9}\)
= \(\dfrac{-7}{9}\)
a) 2/7+-3/8+11/7+1/3+1/7+5/-8
=(2/7+11/7+1/7)+(3/8+-5/8)+1/3
=2+2+1/3
=4+1/3
=13/3
b) -3/8+12/25+5/-8+2/-5+13/25
=(-3/8+-5/8)+(12/25+13/25)+-2/5
=-1+1+-2/5
=0+-2/5
=-2/5
c)7/8+1/8*3/8+1/8*5/8
=7/8+1/8*(3/8+5/8)
=7/8+1/8*1
=7/8+1/8
=1
a) 2/7+-3/8+11/7+1/3+1/7+5/-8
=(2/7+11/7+1/7)+(3/8+-5/8)+1/3
=2+2+1/3
=4+1/3
=13/3
b) -3/8+12/25+5/-8+2/-5+13/25
=(-3/8+-5/8)+(12/25+13/25)+-2/5
=-1+1+-2/5
=0+-2/5
=-2/5
c)7/8+1/8*3/8+1/8*5/8
=7/8+1/8*(3/8+5/8)
=7/8+1/8*1
=7/8+1/8
=1
1.2.3...9 - 1.2.3....8 - 1.2.3....82
= 1.2.3...8(9 - 1 - 8)
= 1.2.3...8.0
= 0
\(1.2.3....9-1.2.3...8-1.2.3....7.8^2\)
\(\Rightarrow1.2.3.4.5.6.7.\left(8.9-8-8^2\right)\)
\(=1.2.3.4.5.6.7.0\)
=0
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