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![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\left(\frac{1-2^2}{2^2}\right)\left(\frac{1-3^2}{3^2}\right)....\left(\frac{1-10^2}{10^2}\right)\)
\(A=\frac{\left(1+2\right)\left(1-2\right)}{2^2}.\frac{\left(1-3\right)\left(1+3\right)}{3^2}.......\frac{\left(1-10\right)\left(1+10\right)}{10^2}\)
\(A=\frac{3.\left(-1\right)}{2^2}.\frac{\left(-2\right).4}{3^2}........\frac{\left(-9\right).11}{10^2}=-\left(\frac{1.3}{2^2}.\frac{2.4}{3^2}....\frac{9.11}{10^2}\right)\)
\(=-\left(\frac{1.2....9}{2.3....10}.\frac{3.4....11}{2.3.4...10}\right)=-\left(\frac{1}{10}.\frac{11}{2}\right)=\frac{-11}{20}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right)....\left(\frac{1}{81}-1\right)\left(\frac{1}{100}-1\right)\)
\(=\frac{-3}{4}.\frac{-8}{9}.\frac{-15}{16}....\frac{-80}{81}.\frac{-99}{100}\)
\(=\left[\left(-1\right).\left(-1\right)...\left(-1\right)\left(9\text{số (-1)}\right)\right].\frac{3}{4}.\frac{8}{9}....\frac{99}{100}\)
\(=\left(-1\right).\frac{1.3}{2.2}.\frac{2.4}{3.3}....\frac{9.11}{10.10}\)
\(=-\frac{1.11}{2.10}=-\frac{11}{10}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right)...\left(\frac{1}{81}-1\right)\left(\frac{1}{100}-1\right)\)
\(=\frac{-3}{4}.\frac{-8}{9}.\frac{-15}{16}.....\frac{-80}{81}.\frac{-99}{100}\)
\(=\left[\left(-1\right).\left(-1\right).\left(-1\right).\left(-1\right).\left(-1\right).\left(-1\right).\left(-1\right).\left(-1\right).\left(-1\right)\right].\frac{3}{4}.\frac{8}{9}.....\frac{99}{100}\)
\(=\left(-1\right).\frac{1.3}{2.2}.\frac{2.4}{3.3}....\frac{9.11}{10.10}\)
\(=-\frac{1.11}{2.10}=-\frac{11}{10}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{9}{8}-\frac{8}{9}+\frac{3}{25}+\frac{1}{4}-\frac{5}{16}+\frac{19}{25}-\frac{1}{9}+\frac{2}{25}-\frac{1}{81}\)
\(A=\left(\frac{9}{8}+\frac{1}{4}-\frac{5}{16}\right)-\left(\frac{8}{9}+\frac{1}{9}-\frac{1}{81}\right)+\left(\frac{3}{25}+\frac{19}{25}+\frac{2}{25}\right)\)
\(A=\frac{17}{16}-\frac{80}{81}+\frac{24}{25}\)
\(A=\frac{33529}{32400}\)