Ta có \(B=\left(\frac{2010}{2}+1\right)+\left(\frac{2009}{3}+1\right)+...+\left(\frac{2}{2010}+1\right)+\left(\frac{1}{2011}+1\right)+1\)

\(B=\frac{2012}{2}+\frac{2012}{3}+...+\frac{2012}{2010}+\frac{2012}{2011}+\frac{2012}{2012}\)

\(B=2012.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}\right)\)

B=2012.A

=>A/B=1/2012

a/b= 1/2012 nha bạn 

tích

bạn ơi tính A đi bạn

Sửa đề:
\(\left(\dfrac{1975}{1976}+\dfrac{2010}{2011}+\dfrac{1963}{1968}\right)\times\left(\dfrac{1}{3}-\dfrac{1}{4}-\dfrac{1}{12}\right)\)
\(=\left(\dfrac{1975}{1976}+\dfrac{2010}{2011}+\dfrac{1963}{1968}\right)\times\dfrac{4-3-1}{12}\)
\(=\left(\dfrac{1975}{1976}+\dfrac{2010}{2011}+\dfrac{1963}{1968}\right)\times\dfrac{0}{12}\)
\(=0\)

2A=1/2+1/6+1/12+1/20+1/30+1/42

    =1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7

    =1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7

    =1-1/7

    =6/7

\(\dfrac{1}{4}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{24}\) + \(\dfrac{1}{40}\) + \(\dfrac{1}{60}\) + \(\dfrac{1}{84}\) + \(x\) = 1

\(\dfrac{1}{2.2}\) + \(\dfrac{1}{2.6}\)+\(\dfrac{1}{2.12}\)+\(\dfrac{1}{2.20}\) + \(\dfrac{1}{2.30}\) + \(\dfrac{1}{2.42}\) +  \(x\) =1

\(\dfrac{1}{2}\).(\(\dfrac{1}{2}\) + \(\dfrac{1}{6}\)+\(\dfrac{1}{12}\)+\(\dfrac{1}{20}\) + \(\dfrac{1}{30}\)+ \(\dfrac{1}{42}\)) + \(x\) = 1

\(\dfrac{1}{2}\).( \(\dfrac{1}{1.2}\) + \(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\)  + \(\dfrac{1}{4.5}\)+ \(\dfrac{1}{5.6}\) + \(\dfrac{1}{6.7}\)) + \(x\) = 1

\(\dfrac{1}{2}\).( \(\dfrac{1}{1}\) - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{7}\)) + \(x\) = 1

\(\dfrac{1}{2}\).( \(\dfrac{1}{1}\) - \(\dfrac{1}{7}\)) + \(x\) = 1

\(\dfrac{1}{2}\).\(\dfrac{6}{7}\) + \(x\) = 1

       \(\dfrac{3}{7}\) + \(x\) = 1 

              \(x\) = 1 -  \(\dfrac{3}{7}\)

               \(x\) = \(\dfrac{4}{7}\)