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$A=\dfrac{\left(\dfrac15-\dfrac27\right)\cdot\dfrac34-\dfrac34\cdot\left(\dfrac13-\dfrac27\right)}{\dfrac15\cdot\dfrac27-\dfrac13\cdot\left(\dfrac27+\dfrac39\right)+\dfrac39+\dfrac15}$
$=\dfrac{\dfrac34\left[\left(\dfrac15-\dfrac27\right)-\left(\dfrac13-\dfrac27\right)\right]}{\dfrac2{35}-\dfrac13\left(\dfrac27+\dfrac13\right)+\dfrac13+\dfrac15}$
$=\dfrac{\dfrac34\left(\dfrac15-\dfrac13\right)}{\dfrac2{35}-\dfrac13\cdot\dfrac{13}{21}+\dfrac13+\dfrac15}$
$=\dfrac{\dfrac34\cdot\left(-\dfrac2{15}\right)}{\dfrac2{35}-\dfrac{13}{63}+\dfrac{8}{15}}$
$=\dfrac{-\dfrac1{10}}{\dfrac{18-65+168}{315}}$
$=\dfrac{-\dfrac1{10}}{\dfrac{121}{315}}$
$=-\dfrac1{10}\cdot\dfrac{315}{121}$
$=-\dfrac{63}{242}.$
\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}...\frac{30}{62}.\frac{31}{64}\)
\(=\frac{1.2.3.4...30.31}{2.2.2.3.2.4.2.5...2.31.2.32}\)
\(=\frac{1.2.3.4...30.31}{2^{31}.\left(2.3.4.5...31\right).32}\)
\(=\frac{1}{2^{31}.32}\)
\(=\frac{1}{2^{31}.2^5}\)
\(=\frac{1}{2^{36}}\)
\(B=\frac{2001}{1}+\frac{2010}{2}+\frac{2009}{3}+...+\frac{2}{2010}+\frac{1}{2001}\)
\(B=\left(2011-1-...-1\right)+\left(\frac{2010}{2}+1\right)+\left(\frac{2009}{3}+1\right)+...+\left(\frac{1}{2011}+1\right)\)
\(B=\frac{2012}{2}+\frac{2012}{3}+...+\frac{2012}{2011}+\frac{2012}{2012}\)
\(B=2012\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2011}+\frac{1}{2012}\right)\)
\(\Rightarrow\)\(\frac{B}{A}=\frac{2012\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2011}+\frac{1}{2012}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2011}+\frac{1}{2012}}=2012\)
Vậy \(\frac{B}{A}=2012\)
Chúc bạn học tốt ~
1/4.2/6.3/8.4/10.........30/62.31/64=4x
=1/2.1/2.1/2.1/2.............1/2.1/64=4^x
=1/2^30.1/2^6=4^x
=1/2^36=4^x
=1/4^18=4^x
=>x=-18
\(1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+\frac{1}{4}.\left(1+2+3+4\right)+...+\frac{1}{20}.\left(1+...+20\right).\)
\(=1+\frac{3}{2}+\frac{6}{3}+\frac{10}{4}+...+\frac{210}{20}\)
\(=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+...+\frac{21}{2}\)
\(=\frac{2+3+4+5+...+21}{2}=\frac{230}{2}=115\)
A = \(\frac{1}{-2}.\frac13+\frac13.\frac{1}{-4}\) + ...+ \(\frac{1}{-9}.\frac{1}{10}\)
A = -(\(\frac12.\) \(\frac13\) + \(\frac13\).\(\frac14\) + ... + \(\frac19\).\(\frac{1}{10}\))
A = -(\(\frac12-\frac13+\frac13-\frac14+\cdots+\frac19-\frac{1}{10}\))
A = - (\(\frac12\) - \(\frac{1}{10}\))
A = - \(\frac25\)