3 câu như nhau cả thôi :v

\(A=\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{55\cdot57}\)

\(A=\frac{1}{2}\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{55\cdot57}\right)\)

\(A=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{55}-\frac{1}{57}\right)\)

\(A=\frac{1}{2}\left(1-\frac{1}{57}\right)\)

\(A=\frac{1}{2}\cdot\frac{56}{57}\)

\(A=\frac{28}{57}\)

\(=5^2\left(\frac{5}{8.13}+\frac{5}{13.18}+...+\frac{5}{93.98}\right).\frac{392}{17}\)

\(=5^2\left(\frac{1}{8}-\frac{1}{13}+\frac{1}{13}-\frac{1}{18}+...+\frac{1}{93}-\frac{1}{98}\right)\frac{392}{17}\)

\(=25\left(\frac{1}{8}-\frac{1}{98}\right)\frac{392}{17}\)

\(=25\times\frac{45}{392}\times\frac{392}{17}\)

\(=25\times\frac{45}{17}\)

\(=\frac{1125}{17}\)

\(5^2.\left(\frac{5}{8.13}+\frac{5}{13.18}+\frac{5}{18.23}+...+\frac{5}{93.98}\right).\frac{392}{5^2}\)

\(\left(\frac{1}{8}-\frac{1}{13}+\frac{1}{13}-\frac{1}{18}+...+\frac{1}{93}-\frac{1}{98}\right).392=\left(\frac{1}{8}-\frac{1}{98}\right).392=45\)

Có:

\(\frac{5^3}{8.13}+\frac{5^3}{13.18}+...+\frac{5^3}{93.98}\)

= \(5^2\left(\frac{5}{8.13}+\frac{5}{13.18}+...+\frac{5}{93.98}\right)\)

=\(25\left(\frac{1}{8}-\frac{1}{13}+\frac{1}{13}-\frac{1}{18}+...+\frac{1}{93}-\frac{1}{98}\right)\)

=\(25\left(\frac{1}{8}-\frac{1}{98}\right)\)

=\(\frac{1125}{392}\)

=> \(\frac{1125}{392}.3\frac{17}{125}\)

= ...

cảm ơn bạn nhá!

\(\frac{10}{3.8}+\frac{10}{8.13}+\frac{10}{13.18}+...+\frac{10}{48.53}\)

\(=\frac{10}{5}\left(\frac{1}{3}-\frac{1}{8}+\frac{1}{8}-\frac{1}{13}+\frac{1}{13}-\frac{1}{18}+...+\frac{1}{48}-\frac{1}{53}\right)\)

\(=2\left(\frac{1}{3}-\frac{1}{53}\right)\)

\(=2.\frac{50}{159}=\frac{100}{159}\)

Ta có: *)A.5=5(1/3.8+1/8.13+...+1/33.38)

                  =5/3.8+5/8.13+...+5/33.38

                  =1/3-1/8+1/8-1/13+...+1/33-1/38

                  =1/3-1/38

=> A=(1/3-1/38).1/5

*)7B=7/3.10+7/10.17+7/17.24+...+7/31.38

       =1/3-1/10+1/10-1/17+...+1/31-1/38

       =1/3-1/38

=>B=(1/3-1/38).1/7

Do đó a/b=(1/5)/(1/7)=7/5

k mk nha!

X=1

Nha bạn 

x=1 nha ban

\(\Rightarrow x\left(\frac{1}{3}-\frac{1}{8}+\frac{1}{8}-\frac{1}{13}+...........+\frac{1}{28}-\frac{1}{33}\right)=\frac{-7}{6}\)

\(\Rightarrow x.\left(\frac{1}{3}-\frac{1}{33}\right)=\frac{-7}{6}\)

\(\Rightarrow x.\frac{10}{33}=\frac{-7}{6}\)

\(\Rightarrow x=\frac{-7}{6}:\frac{10}{33}\)

\(\Rightarrow x=\frac{-231}{60}\)

\(A=\frac{10}{3.8}+\frac{10}{8.13}+\frac{10}{13.18}+\frac{10}{18.23}+\frac{10}{23.28}\)

\(A=2\left(\frac{5}{3.8}+\frac{5}{8.13}+\frac{5}{13.18}+\frac{5}{18.23}+\frac{5}{23.28}\right)\)

\(A=2\left(\frac{1}{3}-\frac{1}{8}+\frac{1}{8}-\frac{1}{13}+...+\frac{1}{23}-\frac{1}{28}\right)\)

\(A=2\left(\frac{1}{3}-\frac{1}{28}\right)\)

\(A=2.\frac{25}{84}=\frac{25}{42}\)

\(A=\frac{10}{3\cdot8}+\frac{10}{8\cdot13}+\frac{10}{13\cdot18}+\frac{10}{18\cdot23}+\frac{10}{23\cdot28}\)

\(A=10\left(\frac{1}{3\cdot8}+\frac{1}{8\cdot13}+\frac{1}{13\cdot18}+\frac{1}{18\cdot23}+\frac{1}{23\cdot28}\right)\)

\(A=\frac{10}{5}\left(\frac{5}{3\cdot8}+\frac{5}{8\cdot13}+\frac{5}{13\cdot18}+\frac{5}{18\cdot23}+\frac{5}{23\cdot28}\right)\)

\(A=2\cdot\left(\frac{1}{3}-\frac{1}{8}+\frac{1}{8}-\frac{1}{13}+\frac{1}{13}-\frac{1}{18}+\frac{1}{18}-\frac{1}{23}+\frac{1}{23}-\frac{1}{28}\right)\)

\(A=2\cdot\left(\frac{1}{3}-\frac{1}{28}\right)\)

\(A=2\cdot\frac{25}{84}\)

\(A=\frac{25}{42}\)

\(A=\frac{10}{3.8}+\frac{10}{8.13}+\frac{10}{13.18}+\frac{10}{18.23}+\frac{10}{23.28}\)

   \(=2\left(\frac{5}{3.8}+\frac{5}{8.13}+\frac{5}{13.18}+\frac{5}{18.23}+\frac{5}{23.28}\right)\)

   \(=2\left(\frac{1}{3}-\frac{1}{8}+\frac{1}{8}-\frac{1}{13}+\frac{1}{13}-\frac{1}{18}+\frac{1}{18}-\frac{1}{23}+\frac{1}{23}-\frac{1}{28}\right)\)

   \(=2\left(\frac{1}{3}-\frac{1}{28}\right)\)

    \(=2.\frac{25}{84}\)

    \(=\frac{25}{42}\)

Study well ! >_<

\(B=\frac{10}{3\cdot8}+\frac{10}{8\cdot13}+\frac{10}{13\cdot18}+\frac{10}{18\cdot23}+\frac{10}{23\cdot28}\)

\(B=2\left[\frac{5}{3\cdot8}+\frac{5}{8\cdot13}+\frac{5}{13\cdot18}+\frac{5}{18\cdot23}+\frac{5}{23\cdot28}\right]\)

\(B=2\left[\frac{1}{3}-\frac{1}{8}+\frac{1}{8}-\frac{1}{13}+...+\frac{1}{23}-\frac{1}{28}\right]\)

\(B=2\left[\frac{1}{3}-\frac{1}{28}\right]=\frac{25}{42}\)

B = 10/3.8 + 10/8.13 + 10/13.18 + 10/18.23 + 10/23.28

   = 2.( 5/3.8 + 5/8.13 + 5/13.18 + 5/18.23 + 10/23.28 )

   = 2.( 1/3 -1/8 + 1/8 - 1/13 + 1/13 - 1/18 + 1/18 - 1/23 + 1/23 - 1/28 )

   = 2.( 1/3 - 1/28 )

   = 2. 25/84

   = 25/42

\(\frac{24}{42}\) nha bn  chúc hc tốtttt