\(\frac{x}{1.3}+\frac{x}{3.5}+\frac{x}{5.7}+....+\frac{x}{97.99}=\frac{49}{99}\)
\(\Leftrightarrow\frac{x}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{97}-\frac{1}{99}\right)=\frac{49}{99}\)
\(\Leftrightarrow\frac{x}{2}.\left(\frac{1}{1}-\frac{1}{99}\right)=\frac{49}{99}\)
\(\Leftrightarrow\frac{x}{2}.\frac{98}{99}=\frac{49}{99}\)
\(\Leftrightarrow\frac{x}{2}=\frac{49}{99}\div\frac{98}{99}\)
\(\Leftrightarrow\frac{x}{2}=\frac{1}{2}\)
\(\Leftrightarrow x=\frac{1}{2}\times2=1\)
\(\frac{x}{1\cdot3}+\frac{x}{3\cdot5}+...+\frac{x}{97\cdot99}=\frac{49}{99}\)
\(\Rightarrow\frac{x}{2}\left[\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+...+\frac{1}{97\cdot99}\right]=\frac{49}{99}\)
\(\Rightarrow\frac{x}{2}\left[\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{97}-\frac{1}{99}\right]=\frac{97}{99}\)
\(\Rightarrow\frac{x}{2}\left[1-\frac{1}{99}\right]=\frac{49}{99}\)
\(\Rightarrow\frac{x}{2}\cdot\frac{98}{99}=\frac{49}{99}\)
\(\Rightarrow\frac{x}{2}=\frac{1}{2}\)
=> x = 1/2 * 2 = 1
