a, Đặt A = \(\frac{9}{5.32}+\frac{9}{8.44}+\frac{9}{11.56}+\frac{9}{14.68}+\frac{9}{17.80}\)
\(=\frac{1}{4}\left(\frac{9}{5.8}+\frac{9}{8.11}+\frac{9}{11.14}+\frac{9}{14.17}+\frac{9}{17.20}\right)\)
\(=\frac{3}{4}\left(\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+\frac{3}{17.20}\right)\)
\(=\frac{3}{4}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}\right)\)
\(=\frac{3}{4}\left(\frac{1}{5}-\frac{1}{20}\right)=\frac{3}{4}\cdot\frac{3}{20}=\frac{9}{80}\)
b, Đặt B = \(\frac{3}{2}-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}\)
\(=\left(1+\frac{1}{2}\right)-\left(\frac{1}{2}+\frac{1}{3}\right)+\left(\frac{1}{3}+\frac{1}{4}\right)-\left(\frac{1}{4}+\frac{1}{5}\right)+\left(\frac{1}{5}+\frac{1}{6}\right)-\left(\frac{1}{6}+\frac{1}{7}\right)\)
\(=1+\frac{1}{2}-\frac{1}{2}-\frac{1}{3}+\frac{1}{3}+\frac{1}{4}-\frac{1}{4}-\frac{1}{5}+\frac{1}{5}+\frac{1}{6}-\frac{1}{6}-\frac{1}{7}\)
\(=1-\frac{1}{7}=\frac{6}{7}\)
