Question

[Bùi Thị Phương Anh]

1/1*3 + 1/3*5 + 1/5*7 + ... + 1/2013*2015 =1/2 - 1/x

    các số trên đều là phân số

Answer 1

[Đức Phạm]

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+....+\frac{1}{2013.2015}=\frac{1}{2}-\frac{1}{x}\)

\(\Leftrightarrow\frac{1}{2}\cdot\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2013}-\frac{1}{2015}\right)=\frac{1}{2}-\frac{1}{x}\)

\(\Leftrightarrow\frac{1}{2}\cdot\left(\frac{1}{1}-\frac{1}{2015}\right)=\frac{1}{2}-\frac{1}{x}\)

\(\Leftrightarrow\frac{1}{2}\cdot\frac{2014}{2015}=\frac{1}{2}-\frac{1}{x}\)

\(\Leftrightarrow\frac{1007}{2015}=\frac{1}{2}-\frac{1}{x}\)

\(\Leftrightarrow\frac{1}{x}=\frac{1}{2}-\frac{1007}{2015}\Leftrightarrow\frac{1}{x}=\frac{1}{4030}\)

\(\Rightarrow x=4030\)