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\(\left(\frac{1}{3\cdot8}+\frac{1}{8\cdot13}+\cdots+\frac{1}{33\cdot38}\right)-x=\frac{31}{114}\)
=>\(\frac15\left(\frac{5}{3\cdot8}+\frac{5}{8\cdot13}+\cdots+\frac{5}{33\cdot38}\right)-x=\frac{31}{114}\)
=>\(\frac15\left(\frac13-\frac18+\frac18-\frac{1}{13}+\cdots+\frac{1}{33}-\frac{1}{38}\right)-x=\frac{31}{114}\)
=>\(\frac15\left(\frac13-\frac{1}{38}\right)-x=\frac{31}{114}\)
=>\(\frac15\cdot\frac{35}{3\cdot38}-x=\frac{31}{114}\)
=>\(\frac{7}{114}-x=\frac{31}{114}\)
=>\(x=\frac{7}{114}-\frac{31}{114}=-\frac{24}{114}=\frac{-4}{19}\)
- B=(1/2).(2/3).(3/4)....(2010/2011).(2011/2012)
B=(1.2.3....2011)/(2.3.4....2012)
B=1/2012
a) \(27^{64}:81^{20}=3^{192}:3^{80}=3^{112}\)
b) \(\left(\dfrac{1}{8}\right)^{20}:\left(\dfrac{1}{16}\right)^9=\left(\dfrac{1}{2}\right)^{60}:\left(\dfrac{1}{2}\right)^{36}=\left(\dfrac{1}{2}\right)^{24}\)
c) \(\dfrac{1}{3}:\dfrac{1}{5}-\dfrac{1}{6}=\dfrac{5}{3}-\dfrac{1}{6}=\dfrac{10}{6}-\dfrac{1}{6}=\dfrac{9}{6}=\dfrac{3}{2}\)