\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{x.\left(x+2\right)}=\frac{8}{7}\)
\(\frac{1}{2}.\left(\frac{1}{1.3}+...+\frac{1}{x.\left(x+y\right)}\right)=\frac{8}{17}\)
\(\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{8}{17}\)
\(\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{x+2}\right)=\frac{8}{17}\)
\(\frac{1}{1}-\frac{1}{x+2}=\frac{8}{17}:\frac{1}{2}\)
\(\frac{1}{1}-\frac{1}{x+2}=\frac{16}{17}\)
\(\frac{1}{x+2}=\frac{1}{1}-\frac{16}{17}=\frac{1}{17}\)
\(\Rightarrow x+2=17\)
\(\Rightarrow x=15\)
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