\(\frac{4}{1.3}+\frac{4}{3.5}+\frac{4}{5.7}+...+\frac{4}{2009.2011}\)
\(=2\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2009.2011}\right)\)
\(=2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{2009}-\frac{1}{2011}\right)\)
\(=2\left(1-\frac{1}{2011}\right)\)
\(=2.\frac{2010}{2011}\)
\(=\frac{4020}{2011}\)
Có:
A=4/1x3+4/3x5+4/5x7+....+4/2009x2011
1/2 x A=1/2x(4/1x3+4/3x5+4/5x7+....+4/2009x2011)
1/2 x A=2/1x3 + 2/3x5 + 2/5x7 +...+ 2/2009x2011
1/2 x A=1-1/3+1/3-1/5+1/5-1/7+.....+1/2009-1/2011
1/2 x A=1 - 1/2011
1/2 x A= 2010/2011
A = 4020/2011
Ủng hộ nha ko ủng hộ thì k
