Question

Tìm x biết  \(x\) /3x5 + \(x\) /5x7+.......+ \(x\) /97x99=16/99

Answer 1

\(\frac{x}{3.5}+\frac{x}{5.7}+...+\frac{x}{97.99}=\frac{16}{99}\)

\(\Rightarrow\frac{x}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\right)=\frac{16}{99}\)

\(\Rightarrow\frac{x}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\right)=\frac{16}{99}\)

\(\Rightarrow\frac{x}{2}\left(\frac{1}{3}-\frac{1}{99}\right)=\frac{16}{99}\)

\(\Rightarrow\frac{x}{2}.\frac{32}{99}=\frac{16}{99}\)

\(\Rightarrow\frac{x}{2}=\frac{16}{99}:\frac{32}{99}=\frac{1}{2}\)

\(\Rightarrow x=1\)

vậy x=1