\(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)
=2.\(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\)
=2.(\(\frac{1}{2}-\frac{1}{2010}\)) = 2.(\(\frac{1005}{2010}-\frac{1}{2010}\))
=2.\(\frac{502}{1005}\)
=\(\frac{1004}{1005}\)
\(=2\left(\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+\frac{2}{6\cdot8}+...+\frac{2}{2008\cdot2010}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+....+\frac{1}{2008}-\frac{1}{2010}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{2010}\right)\)
\(=2\left(\frac{1005}{2010}-\frac{1}{2010}\right)\)
\(=2\cdot\frac{1004}{2010}\)
\(=\frac{1004}{1005}\)
\(k\)\(mk\)\(nha\)\(bn\)
Gọi tổng đó là A Ta có
A:2=2/2x4+2/4x6+...+2/2008x2010
A:2=1/2-1/4+1/4-1/6+...+1/2008-1/2010
A:2=1/2-1/2010
A:2=1004/2010
A=1004/2010x2
A=2008/2010=1004/1005
