Đặt :
\(A=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...............+\dfrac{1}{99.100}\)
\(A=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+..............+\dfrac{1}{99}-\dfrac{1}{100}\)
\(A=\dfrac{1}{2}-\dfrac{1}{100}\)
\(A=\dfrac{49}{100}\)
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