\(\frac{4}{1.3}+\frac{4}{3.5}+\frac{4}{5.7}+...+\frac{4}{2009.2011}\)

\(=2\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2009.2011}\right)\)

\(=2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{2009}-\frac{1}{2011}\right)\)

\(=2\left(1-\frac{1}{2011}\right)\)

\(=2.\frac{2010}{2011}\)

\(=\frac{4020}{2011}\)

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

\(\frac{547}{140}nha\)

HT

TL:

\(=\frac{547}{140}nha\)

_HT_

\(\dfrac{3}{5}+\dfrac{4}{25}=\dfrac{19}{25}\)

\(\dfrac{3}{5}+\dfrac{4}{25}\\ =\dfrac{3x5}{5x5}+\dfrac{4}{25}\\ =\dfrac{15}{25}+\dfrac{4}{25}\\ =\dfrac{19}{25}\)

\(=\dfrac{15}{25}+\dfrac{4}{25}=\dfrac{19}{25}\)

\(5^3.4^2+85.5^3-5^7:5^4=5^3.16+85.5^3-5^3=5^3\left(16+85-1\right)=125.100=12500\)

\(\frac{3}{4}x\frac{4}{5}:\frac{3}{5}x\frac{6}{7}:\frac{1}{7}x\frac{5}{6}\)\(=\)\(\frac{3}{4}x\frac{4}{5}x\frac{5}{3}x\frac{6}{7}x\frac{7}{1}x\frac{5}{6}\)\(=\)\(\frac{3x4x5x6x7x5}{4x5x3x7x1x6}\)\(=\)\(\frac{\left(3\right)x\left(4\right)x\left(5\right)x\left(6\right)x\left(7\right)x5}{\left(3\right)x\left(4\right)x\left(5\right)x\left(6\right)x\left(7\right)x1}\)\(=\)\(\frac{5}{1}\)\(=\)\(5\).

5