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= ( 1 + 3 + 5 + ... + 2011 ) - ( 2 + 6 + 8 + ... + 2010 )
= [ 1006 x ( 2011 + 1 ) : 2 ] - [ 1005 x ( 2010 + 2 ) : 2 ]
= ( 1006 x 2012 : 2 ) - ( 1005 x 2012 : 2 )
= ( 2024072 : 2 ) - ( 2022060 : 2 )
= 1012036 - 1011030
= 1006
\(\frac{1}{10}+\frac{2}{20}+\frac{3}{30}+\frac{4}{40}+\frac{5}{50}+\frac{6}{60}+\frac{7}{70}+\frac{8}{80}+\frac{9}{90}\)
=\(\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}\)
=\(\frac{9}{10}\)
\(\frac{1}{10}+\frac{2}{20}+\frac{3}{30}+\frac{4}{40}+\frac{5}{50}+\frac{6}{60}+\frac{7}{70}+\frac{8}{80}+\frac{9}{90}=\frac{1}{10}+\frac{1}{10}+....+\frac{1}{10}=\frac{9}{10}\)
=(1/11+10/11)+(2/11+9/11)+(3/11+8/11)+(4/11+7/11)+(5/11+6/11)
=11/11+11/11+11/11+11/11+11/11
=1+1+1+1+1
=5
\(5\dfrac{3}{4}:3+2\dfrac{1}{4}\times\dfrac{1}{3}-\dfrac{1}{8}=\left(5\dfrac{3}{4}+2\dfrac{1}{4}\right)\times\dfrac{1}{3}-\dfrac{1}{8}\\ =8\times\dfrac{1}{3}-\dfrac{1}{8}=\dfrac{8}{3}-\dfrac{1}{8}=\dfrac{61}{24}\\ ----\\ \dfrac{3}{5}:\dfrac{5}{6}:\dfrac{6}{7}:\dfrac{7}{8}+\dfrac{2}{5}+\dfrac{23}{35}\\ =\dfrac{3}{5}\times\dfrac{6}{5}\times\dfrac{7}{6}\times\dfrac{8}{7}+\dfrac{2}{5}+\dfrac{23}{35}=\dfrac{18}{25}\times\dfrac{4}{3}+\dfrac{2}{5}+\dfrac{23}{35}=\dfrac{353}{175}\)
=6,96+13,34+19,72+17,98
=20,3+37,7
=58