Tính giá trị biểu thức:
C=\(\dfrac{-1}{7}\)x\(\dfrac{5}{9}\)+\(\dfrac{-5}{9}\)x\(\dfrac{1}{7}\)+\(\dfrac{-5}{9}\)x\(\dfrac{5}{7}\)
D=\(\dfrac{4}{2x3}\)+\(\dfrac{4}{3x4}\)+\(\dfrac{4}{4x5}\)+....+\(\dfrac{4}{8x9}\)
A=\(\dfrac{5}{9}\)-\(\dfrac{5}{8}\)+\(\dfrac{2}{3}\)+\(\dfrac{4}{9}\)+\(\dfrac{-3}{8}\)+\(\dfrac{1}{3}\)
B=\(\dfrac{1}{2}\)+\(\dfrac{1}{6}\)+\(\dfrac{1}{12}\)+\(\dfrac{1}{20}\)+\(\dfrac{1}{30}\)+\(\dfrac{1}{42}\)+\(\dfrac{1}{56}\)
B=\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\)
B=\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}\)
B=\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}\)
B= 1-\(\dfrac{1}{8}\)
B= \(\dfrac{7}{8}\)
\(A=\dfrac{5}{9}-\dfrac{5}{8}+\dfrac{2}{3}+\dfrac{4}{9}+\dfrac{-3}{8}+\dfrac{1}{3}\\ =\dfrac{5}{9}+\dfrac{-5}{8}+\dfrac{2}{3}+\dfrac{4}{9}+\dfrac{-3}{8}+\dfrac{1}{3}\\= \left(\dfrac{5}{9}+\dfrac{4}{9}\right)+\left(\dfrac{2}{3}+\dfrac{1}{3}\right)+\left(\dfrac{-5}{8}+\dfrac{-3}{8}\right)\\ =1+1+\left(-1\right)\\ =2+\left(-1\right)\\ =1\)
\(C=\dfrac{-1}{7}\cdot\dfrac{5}{9}+\dfrac{-5}{9}\cdot\dfrac{1}{7}+\dfrac{-5}{9}\cdot\dfrac{5}{7}\\ =\dfrac{-5}{9}\cdot\left(\dfrac{1}{7}+\dfrac{1}{7}+\dfrac{5}{7}\right)\\ =\dfrac{-5}{9}\cdot1\\ =\dfrac{-5}{9}\)
\(D=\dfrac{4}{2\cdot3}+\dfrac{4}{3\cdot4}+\dfrac{4}{4\cdot5}+...+\dfrac{4}{8\cdot9}\\ =4\cdot\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+...+\dfrac{1}{8\cdot9}\right)\\ =4\cdot\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{8}-\dfrac{1}{9}\right)\\ =4\cdot\left(\dfrac{1}{2}-\dfrac{1}{9}\right)\\ =4\cdot\dfrac{7}{18}\\ =\dfrac{14}{9}\)