Question

[Nguyen Thi Anh Thu]

1, Tìm x

\(\frac{1}{5x7}+\frac{1}{7x9}+\frac{1}{9x11}+.....+\frac{1}{2009x2011}+\frac{1}{x}=\frac{1}{5}x0,5\)

Answer 1

[Đức Phạm]

\(\frac{1}{5.7}+\frac{1}{7\cdot9}+\frac{1}{9\cdot11}+...+\frac{1}{2009\cdot2011}+\frac{1}{x}=\frac{1}{5}\cdot0,5\)

\(=\frac{7-5}{5\cdot7}+\frac{9-7}{7\cdot9}+\frac{11-9}{9\cdot11}+...+\frac{2011-2009}{2009\cdot2011}+\frac{1}{x}=\frac{1}{10}\)

\(=\left[\frac{1}{2}\cdot\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{2009}-\frac{1}{2011}\right)\right]+\frac{1}{x}=\frac{1}{10}\)

\(=\left[\frac{1}{2}\cdot\left(\frac{1}{5}-\frac{1}{2011}\right)\right]+\frac{1}{x}=\frac{1}{10}\)

\(=\left(\frac{1}{2}\cdot\frac{2006}{10055}\right)+\frac{1}{x}=\frac{1}{10}\)

\(=\frac{1003}{10055}+\frac{1}{x}=\frac{1}{10}\)

\(\Rightarrow\frac{1}{x}=\frac{1}{10}-\frac{1003}{10055}\)

\(\frac{1}{x}=\frac{1}{4022}\)

\(\Rightarrow x=1\div\frac{1}{4022}=4022\)