4/2.4 + 4/4.6 + 4/6.8 + ... + 4/2008.2010
= 2.(1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + ... + 1/2008 - 1/2010)
= 2.(1/2 - 1/2010)
= 2.502/1005
= 1004/1005
\(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)
\(=2\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2008.2010}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{2010}\right)\)
\(=2.\frac{502}{1005}\)
\(=\frac{1004}{1005}\)
\(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)
\(=2\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2008.2010}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{2010}\right)=2\left(\frac{1005}{2010}-\frac{1}{2010}\right)=2.\frac{1004}{2010}\)
\(=\frac{1004}{1005}\)
Ta gọi \(\frac{4}{2x4}\)+ \(\frac{4}{4x6}\)+ \(\frac{4}{6x8}\)+ ... + \(\frac{4}{2008x2010}\) là b
=> \(\frac{1}{2}b\)= \(\frac{1}{2}-\frac{1}{4}\)+\(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...-\)\(\frac{1}{2008}+\frac{1}{2010}\)
= \(\frac{1}{2}\)+ \(\frac{1}{2010}\)
=> b =( \(\frac{1}{2}+\frac{1}{2010}\)) x 2
=>b = 1 + \(\frac{1}{1010}\)
=> b = \(1\frac{1}{1010}\)
~~~hk tốt~~~
