\(\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{x\left(x+3\right)}=\frac{101}{1540}\)
\(\Leftrightarrow\frac{1}{3}\left(\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{x\left(x+1\right)}\right)=\frac{101}{1540}\)
\(\Leftrightarrow\frac{1}{3}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{101}{1540}\)
\(\Leftrightarrow\frac{1}{3}\left(\frac{1}{5}-\frac{1}{x+1}\right)=\frac{101}{1540}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{x+1}=\frac{303}{1540}\Rightarrow\frac{1}{x+1}=\frac{1}{308}\)
=> x + 1 = 380 => x = 308 - 1 => x = 307
Vậy x = 307
=1/3(3/5.8+3/8.11+............+1/x(x+3)=101/1540
=.1/3(1/5.8+1/8.11+......1/x(x+3)=101/1540
=1/3(1/5-1/8+1/8-1/11+...........1/x-1/x+3=101/1540
=>1/3(1/5-1/x+3)=101/1540
=>1/5-1/x+3=101/1540 chia 1/3 =303/1540
=>1/x+3= 1/308
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