Question

Tính A = (1/10-1)(1/11-1)(1/12-1)....(1/99-1)(1/100-1)

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Answer 1

\(A=\left(\frac{1}{10}-1\right)\left(\frac{1}{11}-1\right)\left(\frac{1}{12}-1\right)...\left(\frac{1}{99}-1\right)\left(\frac{1}{100}-1\right)\)

\(=\frac{-9}{10}.\frac{-10}{11}.\frac{-11}{12}...\frac{-98}{99}.\frac{-99}{100}\)

\(=-\frac{9.10.11....98.99}{10.11.12...99.100}=-\frac{9}{100}\)