Question

Tìm x biết 1/2x3+1/3x4+.......+1/xx(x+1) =299/600

Answer 1

\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x.\left(x+1\right)}=\frac{299}{600}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{299}{600}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{299}{600}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{299}{600}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{600}\)

\(\Rightarrow x+1=600\)

\(\Rightarrow x=600-1\)

\(\Rightarrow x=599\)

\(Vậy\) \(x=599\)