Đặt:
\(X=\left(1+\dfrac{1}{9}\right)\left(1+\dfrac{1}{10}\right)\left(1+\dfrac{1}{11}\right).....\left(1+\dfrac{1}{200}\right)\)
\(X=\dfrac{10}{9}.\dfrac{11}{10}.\dfrac{12}{11}......\dfrac{201}{200}\)
\(X=\dfrac{10.11.12......201}{9.10.11......200}\)
\(X=\dfrac{201}{9}\)
\(Y=\left(1-\dfrac{1}{10}\right)\left(1-\dfrac{1}{11}\right)\left(1-\dfrac{1}{12}\right).....\left(1-\dfrac{1}{99}\right)\)
\(Y=\dfrac{9}{10}.\dfrac{10}{11}.\dfrac{11}{12}.....\dfrac{98}{99}\)
\(Y=\dfrac{9.10.11......98}{10.11.12.....99}\)
\(Y=\dfrac{9}{99}=\dfrac{1}{11}\)
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