Sau khi thực hiện các phép tính: \(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+.........+\dfrac{1}{97.99}\) , ta có kết quả là
\(\dfrac{49}{99}\). \(\dfrac{98}{99}\). \(\dfrac{50}{99}\). \(\dfrac{1}{2}\). Hướng dẫn giải:\(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+.........+\dfrac{1}{97.99}\)
\(=\dfrac{1}{2}\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...........+\dfrac{2}{97.99}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+........+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{99}\right)\)
\(=\dfrac{1}{2}\left(\dfrac{99}{99}-\dfrac{1}{99}\right)\)
\(=\dfrac{1}{2}.\dfrac{98}{99}=\dfrac{49}{99}\)