Tính giá trị biểu thức: A= 3/2 - 5/6 + 7/12 - 9/20 + 11/30 - 13/42 + 15/56 - 17/72 + 19/90

* Hướng dẫn giải

Ta có: $\frac{3}{2}=\frac{3}{1.2}=\frac{3}{1}-\frac{3}{2}$

$$\begin{gathered} \frac{5}{6}=\frac{5}{2.3}=\frac{5}{2}-\frac{5}{3} \\ \frac{7}{12}=\frac{7}{3.4}=\frac{7}{3}-\frac{7}{4} \\ \frac{9}{20}=\frac{9}{4.5}=\frac{9}{4}-\frac{9}{5} \\ ... \\ \frac{19}{90}=\frac{19}{9.10}=\frac{19}{9}-\frac{19}{10} \end{gathered}$$

$$\begin{gathered} \mathrm{A}=\frac{3}{2}-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90} \\ =\left(\frac{3}{1}-\frac{3}{2}\right)-\left(\frac{5}{2}-\frac{5}{3}\right)+\left(\frac{7}{3}-\frac{7}{4}\right)-\left(\frac{9}{4}-\frac{9}{5}\right)+\left(\frac{11}{5}-\frac{11}{6}\right)-\left(\frac{13}{6}-\frac{13}{7}\right) \\ +\left(\frac{15}{7}-\frac{15}{8}\right)-\left(\frac{17}{8}-\frac{17}{9}\right)+\left(\frac{19}{9}-\frac{19}{10}\right) \\ =3-\frac{3+5}{2}+\frac{5+7}{3}-\frac{7+9}{4}+\frac{9+11}{5}-\frac{11+13}{6}+\frac{13+15}{7} \\ -\frac{15+17}{8}+\frac{17+19}{9}-\frac{19}{10} \\ =3-\frac{8}{2}+\frac{12}{3}-\frac{16}{4}+\frac{20}{5}-\frac{24}{6}+\frac{28}{7}-\frac{32}{8}+\frac{36}{9}-\frac{19}{10} \\ = 3 – 4 + 4 – 4 + 4 – 4 + 4 – 4 + 4 -\frac{19}{10} \\ =3-\frac{19}{10} \\ =\frac{30-19}{10} \\ =\frac{11}{10} \\ \mathrm{Vậy} \mathrm{A}=\frac{11}{10} \end{gathered}$$