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Ta có :
\(A=\frac{4}{1.5}+\frac{5}{5.10}+\frac{6}{10.16}+\frac{7}{16.23}+\frac{8}{23.31}+\frac{9}{31.40}\)
\(A=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{16}+\frac{1}{16}-\frac{1}{23}+\frac{1}{23}-\frac{1}{31}+\frac{1}{31}-\frac{1}{40}\)
\(A=1-\frac{1}{40}=\frac{39}{40}\)
Ủng hộ mk nha !!! ^_^
175 . 1274 - 175 . 273 - 175
= 175 . 1274 - 175 . 273 - 175 . 1
= 175( 1274 - 273 - 1 )
= 175 . 1000
= 175 000
\(174\) x \(1274-175\) x \(273-175\)
\(=221676-47775-175\)
\(=173726\)
N = 1/1x5 + 1/5x10 + 1/10x15 + 1/15x20 + .....+1/2005 x 2010
N = 1 - 1/5 +1/5-1/5+1/10-1/15+1/5-1/20+.....+1/2005-1/2010
N = 1 - 1/2010
N = 2009/2010
Ta có:
\(N=\frac{1}{1x5}+\frac{1}{5x10}+\frac{1}{10x15}...+\frac{1}{2005x2010}\)
\(\Rightarrow Nx5=\left(\frac{1}{1x5}+\frac{1}{5x10}+\frac{1}{10x15}...+\frac{1}{2005x2010}\right)x5\)
\(=\frac{5}{1x5}+\frac{5}{5x10}+\frac{5}{10x15}...+\frac{5}{2005x2010}\)
\(=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+...+\frac{1}{2005}-\frac{1}{2010}\)
\(=1-\frac{1}{2010}\)
\(=\frac{2009}{2010}\)
\(\Rightarrow N=\frac{2009}{2010}:5=\frac{2009}{2010}x\frac{1}{5}=\frac{2009}{10050}\)