Question

1/5.8 +1/8.11+1/1.14+.....+ 1/x.(x+3)=101/1540

Answer 1

\(\dfrac{1}{5\cdot8}+\dfrac{1}{8\cdot11}+...+\dfrac{1}{x\left(x+3\right)}=\dfrac{101}{1540}\)

=>\(\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+...+\dfrac{3}{x\left(x+3\right)}=\dfrac{303}{1540}\)

=>\(\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{x}-\dfrac{1}{x+3}=\dfrac{303}{1540}\)

=>\(\dfrac{1}{5}-\dfrac{1}{x+3}=\dfrac{303}{1540}\)

=>\(\dfrac{1}{x+3}=\dfrac{1}{5}-\dfrac{303}{1540}=\dfrac{1}{308}\)

=>x+3=308

=>x=305