Jmgoxpig och ogu o chxjf yvb

8vuob 

Đặt: \(A=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{2011.2013}\)

\(=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{2011.2013}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2011}-\frac{1}{2013}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{2013}\right)\)

\(=\frac{1}{2}.\frac{2012}{2013}\)

\(=\frac{1006}{2013}\)

-3/4+3/4* (x-1/2)+1/6=-1

=0*(x-1/2)=-7/6

nên ko tìm đc x

ta có x =0

nhớ ghi rõ cách làm ( tính nhanh )

Ta có : \(\frac{3}{5}+\frac{6}{11}+\frac{7}{13}+\frac{2}{5}+\frac{5}{11}+\frac{19}{13}+\frac{1}{2}+\frac{2}{3}-\frac{1}{6}\)

\(=\left(\frac{3}{5}+\frac{2}{5}\right)+\left(\frac{6}{11}+\frac{5}{11}\right)+\left(\frac{7}{13}+\frac{19}{13}\right)+\left(\frac{1}{2}+\frac{2}{3}-\frac{1}{6}\right)\)

\(=1+1+2+1=5\)

\(\frac{3}{5}+\frac{6}{11}+\frac{7}{13}+\frac{2}{5}+\frac{5}{11}+\frac{19}{13}:\frac{1}{2}+\frac{2}{3}-\frac{1}{6}\)

\(=\left(\frac{3}{5}+\frac{2}{5}\right)+\left(\frac{19}{13}-\frac{7}{13}\right)+\left(\frac{6}{11}+\frac{5}{11}\right):\frac{2}{3}+\frac{1}{6}\)

\(=1+1+1:\frac{2}{3}+\frac{1}{6}\)

\(=3:\frac{2}{3}+\frac{1}{6}\)

\(=\frac{9}{2}+\frac{1}{6}\)

\(=\frac{14}{3}\)