Đặt: \(A=\dfrac{1}{99}-\dfrac{1}{99\cdot97}-\dfrac{1}{97\cdot95}-....-\dfrac{1}{3\cdot1}\)
\(2A=\dfrac{2}{99}-\dfrac{2}{99\cdot97}-\dfrac{2}{97\cdot95}-...-\dfrac{2}{3\cdot1}\)
\(2A=\dfrac{2}{99}-\left(\dfrac{2}{99\cdot97}+\dfrac{2}{97\cdot95}+...+\dfrac{2}{3\cdot1}\right)\)
\(2A=\dfrac{2}{99}-\left(\dfrac{1}{97}-\dfrac{1}{99}+\dfrac{1}{95}-\dfrac{1}{97}+...+\dfrac{1}{3}-\dfrac{1}{5}+1-\dfrac{1}{3}\right)\)
\(2A=\dfrac{2}{99}-\left(-\dfrac{1}{99}+1\right)\)
\(2A=\dfrac{2}{99}-\dfrac{98}{99}\)
\(2A=-\dfrac{439}{99}\)
\(A=-\dfrac{439}{99}:2\)
\(A=-\dfrac{439}{198}\)
1/99 - 1/99.97 - 1/97.95 - ... - 1/3.1
= 1/99 - 1/2.(1/97 - 1/99 + 1/95 - 1/97 + ... + 1 - 1/3)
= 1/99 - 1/2.(1 - 1/99)
= 1/99 - 1/2 . 98/99
= 1/99 - 49/99
= -48/99
