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21 tháng 6 2016

\(=\frac{3}{3.13}+\frac{3}{13.23}+...+\frac{3}{1993.2003}\)

\(=\frac{1}{10}.\left(1-\frac{3}{13}+\frac{3}{13}-\frac{3}{23}+...+\frac{3}{1993}-\frac{3}{2003}\right)\)

\(=\frac{1}{10}.\left(1-\frac{3}{2003}\right)\)

\(=\frac{1}{10}.\frac{2000}{2003}\)

\(=\frac{200}{2003}\)

21 tháng 6 2016

Đặt \(A=\frac{1}{13}+\frac{3}{13.23}+\frac{3}{23.33}+...+\frac{3}{1993.2003}\)

\(\Rightarrow A=\frac{3}{3.13}+\frac{3}{13.23}+\frac{3}{23.33}+...+\frac{3}{1993.2003}\)

\(\Rightarrow A=3\left(\frac{1}{3.13}+\frac{1}{13.23}+\frac{1}{23.33}+...+\frac{1}{1993.2003}\right)\)

\(\Rightarrow A=\frac{3}{10}\left(\frac{10}{3.13}+\frac{10}{13.23}+\frac{10}{23.33}+...+\frac{10}{1993.2003}\right)\)

\(\Rightarrow A=\frac{3}{10}\left(\frac{1}{3}-\frac{1}{13}+\frac{1}{13}-\frac{1}{23}+\frac{1}{23}-\frac{1}{33}+...+\frac{1}{1993}-\frac{1}{2003}\right)\)

\(\Rightarrow A=\frac{3}{10}\left(\frac{1}{3}-\frac{1}{2003}\right)\)

\(\Rightarrow A=\frac{3}{10}.\left(\frac{2003}{6009}-\frac{3}{6009}\right)\)

\(\Rightarrow A=\frac{3}{10}.\frac{2000}{6009}\)

\(\Rightarrow A=\frac{200}{2003}\)

29 tháng 7 2021

 \(N=\frac{1}{13}+\frac{3}{13.23}+\frac{3}{23.33}+...+\frac{3}{1993.2003}\)

\(=\frac{3}{3.13}+\frac{3}{13.23}+\frac{3}{23.33}+...+\frac{3}{1993.2003}\)

\(=\frac{3}{10}\left(\frac{10}{3.13}+\frac{10}{13.23}+\frac{10}{23.33}+..+\frac{10}{1993.2003}\right)\)

\(=\frac{3}{10}\left(\frac{1}{3}-\frac{1}{13}+\frac{1}{13}-\frac{1}{23}+\frac{1}{23}-\frac{1}{33}+...+\frac{1}{1993}-\frac{1}{2003}\right)\)

\(=\frac{3}{10}\left(\frac{1}{3}-\frac{1}{2003}\right)=\frac{3}{10}.\frac{2000}{6009}=\frac{200}{2003}\)

29 tháng 7 2021

\(N=\)\(\frac{1}{13}\)\(+\)\(\frac{3}{13.23}\)\(+\)\(\frac{3}{23.33}\)\(+...+\)\(\frac{3}{1993.2003}\)

\(N=\)\(\frac{1}{13}\)\(+\)\(\left(\frac{3}{13.23}+\frac{3}{23.33}+...+\frac{3}{1993.2003}\right)\)

\(N=\)\(\frac{1}{13}\)\(+\)\(\left[\frac{3}{10}\left(\frac{1}{13.23}+\frac{1}{23.33}+...+\frac{1}{1993.2003}\right)\right]\)

\(N=\)\(\frac{1}{13}\)\(+\)\(\left[\frac{3}{10}\left(\frac{1}{13}-\frac{1}{23}+\frac{1}{23}-\frac{1}{33}+...+\frac{1}{1993}-\frac{1}{2003}\right)\right]\)

\(N=\)\(\frac{1}{13}\)\(+\)\(\left[\frac{3}{10}\left(\frac{1}{13}-\frac{1}{2003}\right)\right]\)

\(N=\)\(\frac{1}{13}\)\(+\)\(\left[\frac{3}{10}.\frac{1990}{26039}\right]\)

\(N=\)\(\frac{1}{13}\)\(+\)\(\frac{597}{26039}\)

\(N=\)\(\frac{200}{2003}\)

24 tháng 6 2017

\(\frac{1}{13}+\frac{3}{13\cdot23}+\frac{3}{23\cdot33}+...+\frac{3}{1993\cdot2003}\)

\(=\frac{1}{13}+\left[\frac{3}{13\cdot23}+\frac{3}{23\cdot33}+...+\frac{3}{1993\cdot2003}\right]\)

\(=\frac{1}{13}+\left[\frac{3}{10}\left[\frac{1}{13\cdot23}+\frac{1}{23\cdot33}+...+\frac{1}{1993\cdot2003}\right]\right]\)

\(=\frac{1}{13}+\left[\frac{3}{10}\left[\frac{1}{13}-\frac{1}{23}+\frac{1}{23}-\frac{1}{33}+...+\frac{1}{1993}-\frac{1}{2003}\right]\right]\)

\(=\frac{1}{13}+\left[\frac{3}{10}\left[\frac{1}{13}-\frac{1}{2003}\right]\right]\)

\(=\frac{1}{13}+\left[\frac{3}{10}\cdot\frac{1990}{26039}\right]\)

\(=\frac{1}{13}+\frac{597}{26039}\)

\(=\frac{200}{2003}\)

24 tháng 6 2017

Đặt A= 1/13 + 3/13.23 + 3/ 23.33 + ... + 3/1993.2003 

A- 1/13 = 3/13.23 + 3/ 23.33 + ... + 3/1993.2003 

10/3 ( A-1/3) =  10/3. (3/13.23 + 3/ 23.33 + ... + 3/1993.2003) 

10/3A - 10/9 = 10/13.23 + 10/ 23.33 + ... + 10/1993.2003 

10/3A - 10/9  = 1/13 - 1/23 + 1/23 - 1/33 +...+ 1/1993- 1/2003

10/3A = 1/13 - 1/2003 + 10/9

10/3 A= ? 

đến đây bn tự làm nha

10/3A - 10/9 = 1/13 

\(E=\frac{2}{3.5}+\frac{7}{5.12}+\frac{9}{4.39}=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{12}+\frac{27}{12.39}=\frac{1}{3}-\frac{1}{12}+\frac{1}{12}-\frac{1}{39}=\frac{1}{3}-\frac{1}{39}=\frac{4}{13}\)

 

7 tháng 9 2015

lộn bạn đăng từng câu thôi

1 tháng 4 2017

\(B=\frac{7}{3.13}+\frac{7}{13.23}+...+\frac{7}{53.63}\)

\(B=10.\left(\frac{1}{3.13}+\frac{1}{13.23}+....+\frac{1}{53.63}\right)\)

\(B=10.\left(\frac{1}{3}-\frac{1}{13}+\frac{1}{13}-\frac{1}{23}+...+\frac{1}{53}+\frac{1}{63}\right)\)

\(B=10.\left(\frac{1}{3}-\frac{1}{63}\right)\)

\(B=10.\frac{20}{63}\)

\(B=\frac{200}{63}\)

1 tháng 4 2017

Cảm ơn bn nha

9 tháng 5 2016

\(\frac{7}{3.13}+\frac{7}{13.23}+\frac{7}{23.33}+\frac{7}{33.43}\)

\(=\frac{7}{10}\left(\frac{10}{3.13}+\frac{10}{13.23}+\frac{10}{23.33}+\frac{10}{33.43}\right)\)

\(=\frac{7}{10}\left(\frac{1}{3}-\frac{1}{13}+\frac{1}{13}-\frac{1}{23}+\frac{1}{23}-\frac{1}{33}+\frac{1}{33}-\frac{1}{43}\right)\)

\(=\frac{7}{10}\left(\frac{1}{3}-\frac{1}{43}\right)\)

\(=\frac{7}{10}\left(\frac{43}{129}-\frac{3}{129}\right)\)

\(=\frac{7}{10}.\frac{40}{129}\)

\(=\frac{28}{129}\)

mk làm đúng rồi nha, ko tin bấm thử máy tính

9 tháng 5 2016

 7/3.13 + 7/13.23 + 7/23.33 + 7/33.43

= 7/10.(1/3-1/13+1/13-1/23+1/23-1/33+1/33-1/43)

= 7/10.(1/3-1/43)

= 7/10 . 14/43

= 49/215