Câu trả lời:
\(M=\frac{1}{3}.\left(\frac{1}{5}-\frac{1}{8}+...+\frac{1}{x}-\frac{1}{x+3}\right)\)
\(M=\frac{1}{3}.\left(\frac{1}{5}-\frac{1}{x+3}\right)\)
Thay M vào ta có :
\(\frac{1}{3}.\left(\frac{1}{5}-\frac{1}{x+3}\right)=\frac{101}{1540}\)
=> \(\left(\frac{1}{x}-\frac{1}{x+3}\right)=\frac{101}{1540}:\frac{1}{3}\)
=> \(\frac{1}{1}-\frac{1}{x+3}=\frac{303}{1540}\)
=> \(\frac{1}{x+3}=\frac{1}{1}-\frac{303}{1540}\)
=> \(\frac{1}{x+3}=\frac{1237}{1540}\)
=> x+3 = 1540
=> x = 1537