\(\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}+\frac{1}{9x11}+\frac{1}{11x13}\)
\(=\frac{1}{2}x\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{1}{2}x\left(\frac{1}{3}-\frac{1}{13}\right)\)
\(=\frac{1}{2}x\frac{10}{39}\)
\(=\frac{5}{39}\)
\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}\)
\(=\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{13}\right)\)
\(=\frac{1}{2}\cdot\frac{10}{39}=\frac{5}{39}\)
Đặt A=\(\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}+...+\frac{1}{11x13}\)
Ax2=\(2x\left(\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}+...+\frac{1}{11x13}\right)\)
Ax2=\(\frac{2}{3x5}+\frac{2}{5x7}+\frac{2}{7x9}+...+\frac{2}{11x13}\)
Ax2=\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\)
Ax2=\(\frac{1}{3}-\frac{1}{13}\)
Ax2=\(\frac{10}{39}\)
=>A=\(\frac{5}{39}\)
~~~hok tốt~~~
<br class="Apple-interchange-newline"><div id="inner-editor"></div>13.5 +15.7 +17.9 +19.11 +111.13
=12 ·(13 −15 +15 −17 +17 −19 +19 −111 +111 −113 )
=12 ·(13 −113 )
=12 ·1039 =539
Đặt biểu thức trên là A . Ta có:
A=\(\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}+\)\(\frac{1}{9\times11}+\frac{1}{11\times13}\)
2A = \(\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}\)\(+\frac{2}{9\times11}+\frac{2}{11\times13}\)
= \(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}\)\(+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)\(+\frac{1}{11}-\frac{1}{13}\)
= \(\frac{1}{3}-\frac{1}{13}\)
= \(\frac{10}{39}\)
\(\Rightarrow A=\frac{10}{39}:2\)
= \(\frac{5}{39}\)
\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}\)
= \(\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
=\(\frac{1}{2}\left(\frac{1}{3}-\frac{1}{13}\right)\)
= \(\frac{1}{2}.\frac{10}{39}\)
= \(\frac{10}{78}\)=\(\frac{5}{39}\)
