\(\frac{1}{5\cdot8}+\frac{1}{8\cdot11}+...+\frac{1}{x\left(x+3\right)}=\frac{101}{1540}\) (dấu . là nhân nhé)
=> \(\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{x}-\frac{1}{x+3}\right):3=\frac{101}{1540}\)
=> \(\left(\frac{1}{5}-\frac{1}{x+3}\right):3=\frac{101}{1540}\)
=> \(\frac{1}{5}-\frac{1}{x+3}=\frac{101}{1540}\cdot3=\frac{303}{1540}\)
=> \(\frac{1}{x+3}=\frac{1}{5}-\frac{303}{1540}=\frac{1}{308}\)
=> \(x+3=308\Rightarrow x=308-3=305\)
\(\frac{1}{5x8}+\frac{1}{8x11}+...+\frac{1}{Xx\left(X+3\right)}=\frac{101}{1540}\)
<=>\(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{x}-\frac{1}{x+3}=\frac{101}{1540}\)
<=>\(\frac{1}{5}-\frac{1}{x+3}=\frac{101}{1540}\)
<=>\(\frac{x-2}{5x+15}=\frac{101}{1540}\)
<=>1540x-3080=505x+1515
<=>1035x=4595
<=>x=919/207
