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\(\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+....+\frac{1}{2009\cdot2010}\right)\cdot x=2009\)
\(\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2009}-\frac{1}{2010}\right)\cdot x=2009\)
\(\left(1-\frac{1}{2010}\right)\cdot x=2009\)
\(\frac{2009}{2010}\cdot x=2009\)
\(x=2009:\frac{2009}{2010}\)
\(x=2010\)
\(\frac{x}{2}\cdot3+4x=23,1\)
\(\Leftrightarrow x\cdot\frac{3}{2}+4\cdot x=23,1\)
\(\Leftrightarrow x\left(\frac{3}{2}+4\right)=23,1\)
\(\Leftrightarrow x\cdot\frac{11}{2}=23,1\)
\(\Leftrightarrow x=4,2\)
x . 1/4 + x . 1/5 + x . 2 = 19,6
x . ( 1/4 + 1/5 + 2 ) = 19,6
x . 49/20 = 19,6
x = 19,6 : 49/20
x = 8
\(2\frac{3}{13}\cdot\frac{26}{58}\cdot4\cdot2\frac{15}{24}\cdot\frac{8}{21}=\frac{29}{13}\cdot\frac{26}{58}\cdot4\cdot\frac{21}{8}\cdot\frac{8}{21}=\frac{29\cdot26\cdot4\cdot21\cdot8}{13\cdot58\cdot8\cdot21}=\frac{1\cdot2\cdot4\cdot1\cdot1}{1\cdot2\cdot1\cdot1}=\frac{1\cdot4}{1}=4\)
( 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 +1/5.6 ) x 10 - x = 0
= ( 1- 1/2 +1/2 -1/3 +1/3 - 1/4 + 1/4 - 1/5 +1/5 -1/6 ) x 10 - x = 0
= ( 1 - 1/6 ) x 10 - x = 0
= 5/6 x 10 - x =0
= 25/3 - x =0
x = 25/3 - 0
x = 25/3
\(\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\right)\times10-x=0\)
\(\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\times10-x=0\)
\(\left(\frac{1}{1}-\frac{1}{6}\right)\times10-x=0\)
\(\frac{5}{6}\times10-x=0\)
\(\frac{25}{3}-x=0\)
x =\(\frac{25}{3}-0=\frac{25}{3}\)