\(\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}+..........+\frac{1}{97x99}\)
= \(1-\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-........-\frac{1}{97}+\frac{1}{97}-\frac{1}{99}\)
= \(1-\frac{1}{3}-\frac{1}{99}\)
= \(\frac{99}{99}-\frac{33}{99}-\frac{1}{99}\)
= \(\frac{65}{99}\)
\(\frac{1}{3}\)*5+\(\frac{1}{5}\)*7+\(\frac{1}{7}\)*9*...*\(\frac{1}{97}\)*99
=\(\frac{5}{3}\)*\(\frac{7}{5}\)*\(\frac{9}{7}\)*...*\(\frac{99}{97}\)
=\(\frac{99}{3}\)
đúng thì nha
\(\frac{1}{3\cdot5}\)+\(\frac{1}{5\cdot7}\)+\(\frac{1}{7\cdot9}\)+..+\(\frac{1}{97\cdot99}\)
=\(\frac{1\cdot2}{3\cdot5\cdot2}\)+\(\frac{1\cdot2}{5\cdot7\cdot2}\)+\(\frac{1\cdot2}{7\cdot9\cdot2}\)+..+\(\frac{1\cdot2}{97\cdot99\cdot2}\)
=\(\frac{1}{2}\)*(\(\frac{2}{3\cdot5}\)+\(\frac{2}{5\cdot7}\)+\(\frac{2}{7\cdot9}\)+...+\(\frac{2}{97\cdot99}\))
=\(\frac{1}{2}\)*(\(\frac{1}{3}\)-\(\frac{1}{5}\)+\(\frac{1}{5}\)-\(\frac{1}{7}\)+\(\frac{1}{7}\)-\(\frac{1}{9}\)+..+\(\frac{1}{97}\)-\(\frac{1}{99}\))
=\(\frac{1}{2}\)*(\(\frac{1}{3}\)-\(\frac{1}{99}\))
=\(\frac{1}{2}\)*(\(\frac{33}{99}\)-\(\frac{1}{99}\))
=\(\frac{1}{2}\)*\(\frac{32}{99}\)
=\(\frac{32}{198}\)
