\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{91.93}+\frac{1}{x}=5\)
\(\Rightarrow\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{91.93}\right)+\frac{1}{x}=5\)
\(\Rightarrow\left[\frac{1}{2}\times\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{91.93}\right)\right]+\frac{1}{x}=5\)
\(\Rightarrow\left[\frac{1}{2}\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{91}-\frac{1}{93}\right)\right]+\frac{1}{x}=5\)
\(\Rightarrow\left[\frac{1}{2}\times\left(1-\frac{1}{93}\right)\right]+\frac{1}{x}=5\)
\(\Rightarrow\left[\frac{1}{2}\times\frac{92}{93}\right]+\frac{1}{x}=5\)
\(\Rightarrow\frac{46}{93}+\frac{1}{x}=5\)
\(\Rightarrow\frac{1}{x}=5-\frac{46}{93}\)
\(\Rightarrow\frac{1}{x}=\frac{419}{93}\)
\(\Rightarrow x=1:\frac{419}{93}\)
\(\Rightarrow x=\frac{93}{419}\)
Vậy \(x=\frac{93}{419}\)
_Chúc bạn học tốt_
