Question

1/(5*8)+1/(8*11)+..........+x/(x*(x+3))=101/1540

x=?

Answer 1

\(3.\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{x}-\frac{1}{x+3}\right)=\frac{101}{1540}\)

\(3.\left(\frac{1}{5}-\frac{1}{x+3}\right)=\frac{101}{1540}\)

\(\frac{1}{5}-\frac{1}{x+3}=\frac{101}{4620}\)

\(\frac{1}{x+3}=...\)  (tự làm tiếp)

Answer 2

\(\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{x\left(x+1\right)}=\frac{101}{1540}\)

\(\frac{1}{3}.\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{101}{1540}\)

\(\frac{1}{5}-\frac{1}{x+1}=\frac{101}{1540}:\frac{1}{3}=\frac{303}{1540}\)

\(\frac{1}{x+1}=\frac{1}{5}-\frac{303}{1540}=\frac{1}{308}\)

=> x + 1 = 308

=> x = 308 - 1

=> x = 307