\(=\frac{4}{2x4}+\frac{4}{4x6}+\frac{4}{6x8}+...+\frac{4}{18x20}\)
\(=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{18}-\frac{1}{20}\right)\)
\(=2x\left(\frac{1}{2}-\frac{1}{20}\right)\\ =2x\frac{9}{20}\\ =\frac{9}{10}\)
4/8+4/24++4/48+4/80+...+4/288+4/260
=4/2.4+4/4.6+4/6.8+4/8.10+...+4/16.18+4/18.20
=2.( 2/2.4+2/4.6+2/6.8+ 2/8.10+...+1/16-1/18+1/18-1/20
=2.( 1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+...+1/16-1/18+1/18-1/20)
=2.( 1/2 -1/20)
=2.9/20
= 9/10
. la` nha^n
\(\frac{4}{8}+\frac{4}{24}+\frac{4}{48}+\frac{4}{80}+...+\frac{4}{288}+\frac{4}{360}\)
\(=2\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+...+\frac{2}{16.18}+\frac{2}{18.20}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+...+\frac{1}{18}-\frac{1}{20}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{20}\right)\)
\(=2.\frac{9}{20}\)
\(=\frac{9}{10}\)