Question

Tìm x biết:

\(\frac{1}{1\cdot3}\)+\(\frac{1}{3\cdot5}\)+ \(\frac{1}{5\cdot7}\)+\(\frac{1}{7\cdot9}\)+ .........+\(\frac{1}{\left(2x-1\right)\cdot\left(2x+1\right)}\)= \(\frac{49}{99}\)

Answer 1

\(\frac{1}{1\cdot3}\)+\(\frac{1}{3\cdot5}\)+\(\frac{1}{5\cdot7}\)+\(\frac{1}{7\cdot9}\)+.............+\(\frac{1}{\left(2x-1\right)+\left(2x+1\right)}\)=\(\frac{49}{99}\)

 

 =>2(\(\frac{1}{1\cdot3}\)+\(\frac{1}{3\cdot5}\)+\(\frac{1}{5\cdot7}\)+\(\frac{1}{7\cdot9}\)+.............+\(\frac{1}{\left(2x-1\right)+\left(2x+1\right)}\))=\(\frac{49}{99}\)*2=> 1-\(\frac{1}{2x+1}\)=\(\frac{98}{99}\)\(\frac{1}{2x+1}\)=1-\(\frac{98}{99}\)\(\frac{1}{2x+1}\)= \(\frac{1}{99}\)=> 2x+1=992x=99-12x=98x=98/2x=49