1. Tính nhanh:
A= (\(1-\frac{1}{9}\))x(\(1-\frac{1}{16}\))x(\(1-\frac{1}{25}\)) ..... (\(1-\frac{1}{361}\))x(\(1-\frac{1}{400}\))
B= (\(1+\frac{1}{8}\))x(\(1+\frac{1}{15}\))x(\(1+\frac{1}{24}\)) ... (\(1+\frac{1}{440}\))x(\(1+\frac{1}{483}\))
C= \(\frac{17}{23}x\frac{7}{61}+\frac{17}{23}x\frac{28}{61}+\frac{17}{23}x\frac{26}{61}\)
\(A=\frac{8}{9}\cdot\frac{15}{16}\cdot\frac{24}{25}\cdot...\cdot\frac{360}{361}\cdot\frac{399}{400}\)
\(A=\frac{2\cdot4\cdot3\cdot5\cdot4\cdot6\cdot...\cdot18\cdot20\cdot19\cdot21}{3\cdot3\cdot4\cdot4\cdot5\cdot5\cdot...\cdot19\cdot19\cdot20\cdot20}\)
\(A=\frac{2\cdot21}{3\cdot20}\)
\(A=\frac{7}{10}\)
\(B=\frac{9}{8}\cdot\frac{16}{15}\cdot\frac{25}{24}\cdot...\cdot\frac{441}{440}\cdot\frac{484}{483}\)
\(B=\frac{3\cdot3\cdot4\cdot4\cdot5\cdot5\cdot...\cdot21\cdot21\cdot22\cdot22}{2\cdot4\cdot3\cdot5\cdot4\cdot6\cdot...\cdot20\cdot22\cdot21\cdot23}\)
\(B=\frac{3\cdot22}{2\cdot23}=\frac{33}{23}\)
\(C=\frac{17}{23}.\left(\frac{7}{61}+\frac{28}{61}+\frac{26}{61}\right)\)
\(C=\frac{17}{23}\cdot1=\frac{17}{23}\)
