Đặt \(A=\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{602.605}\)

\(A=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{602}-\frac{1}{605}\)

\(A=\frac{1}{5}-\frac{1}{605}\)

\(A=\frac{24}{121}\)

\(\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+...+\frac{3}{602\cdot605}\)

\(=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{602}-\frac{1}{605}\)

\(=\frac{1}{5}-\frac{1}{605}+0+...+0\)

\(=\frac{24}{121}\)

\(=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{602}-\frac{1}{605}\)

\(=\frac{1}{5}-\frac{1}{605}\)

\(F=\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{2006.2009}\)

\(F=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{2006}-\frac{1}{2009}\)

\(F=\frac{1}{5}-\frac{1}{2009}\)

\(F=\frac{2004}{10045}\)

\(F=\frac{3}{5.8}+\frac{3}{8.11}+\frac{1}{11.14}+...+\frac{3}{2006.2009}\)

\(F=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{2006}-\frac{1}{2009}\)

\(F=\frac{1}{5}-\frac{1}{2009}\)

\(F=0\)

F = 1/5 - 1/8 + 1/8 - 1/11 +,,,+1/2006 - 1/2009
F = 1/5 - 1/2009
F = 2008/10044
Chúc bạn học tốt 

\(\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+\frac{3}{11\cdot14}+\frac{3}{14\cdot17}=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{14}-\frac{1}{17}\)

\(=\frac{1}{2}-\frac{1}{17}=\frac{15}{34}\)

Tính

\(\frac{3}{2\times5}+\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}+\frac{3}{14\times17}\)

\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)

\(=\frac{1}{2}-\frac{1}{17}=\frac{17}{34}-\frac{2}{34}=\frac{15}{34}\)

Ta có: Biểu thức trên sẽ =

\(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)1/17 (nó bị lỗi nên k viết đc T_T)

= \(\frac{1}{2}-\frac{1}{17}=\frac{15}{34}\)

Chúc bạn học tốt!~

\(G=\frac{1}{1.2}+\frac{2}{2.4}+\frac{3}{4.7}+\frac{4}{7.11}+\frac{5}{11.16}\)

\(G=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}\)

\(G=1-\frac{1}{16}\)

\(G=\frac{15}{16}\)

\(G=\frac{1}{1.2}+\frac{2}{2.4}+\frac{3}{4.7}+\frac{4}{7.11}+\frac{5}{11.16}\)

\(G=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}\)

\(G=1-\frac{1}{16}\)

\(G=\frac{15}{16}\)

\(G=\frac{1}{1.2}+\frac{2}{2.4}+\frac{3}{4.8}+\frac{4}{7.11}+\frac{5}{11.16}\)

\(G=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}\)

\(G=1-\frac{1}{16}=\frac{15}{16}\)

\(B=\frac{5}{2}+\left(\frac{4}{1.11}+\frac{3}{11.2}\right)+\left(\frac{1}{2.15}+\frac{13}{15.4}\right)\)

\(B=\frac{5}{2}+\frac{1}{11}.\left(4+\frac{3}{2}\right)+\frac{1}{15}\left(\frac{1}{2}+\frac{13}{4}\right)=\frac{5}{2}+\frac{1}{11}.\frac{11}{2}+\frac{1}{15}.\frac{15}{4}\)

=> \(B=\frac{5}{2}+\frac{1}{2}+\frac{1}{4}=\frac{10}{4}+\frac{2}{4}+\frac{1}{4}=\frac{13}{4}\)

Ta có

1/7.B = 5/2.7 + 4/7.11 + 3/11.14 + 1/14.15 + 13/15.28

1/7.B = 1/2 - 1/7 + 1/7 - 1/11 + 1/11 - 1/14 + 1/14 - 1/15 + 1/15 - 1/28

1/7.B = 1/2 - 1/28

1/7.B = 14/28 - 1/28

1/7.B = 13/28

B = 13/28 : 1/7

B = 13/28 . 7

B = 13/4

Ta có :

\(B=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)

\(B=7\left(\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\right)\)

   \(=7\left(\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\right)\) 

     \(=7\left(\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}\right)\)

      \(=7\left(\frac{1}{2}-\frac{1}{28}\right)\)

      \(=7.\frac{13}{28}\)

      \(=\frac{13}{4}\)

B = \(\left(\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\right)\))

B = 7 . \(\left(\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\right)\)

B = 7 . \(\left(\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}\right)\)

B = 7 . ( 1/2 - 1/28 )

B = 7 . 13/28

B = 13/4

1/7B= 5/2.7 + 4/7.11 + 3/11.14 + 1/14.15 + 13/15.28

1/7B= 1/2 - 1/7 + 1/7 - 1/11 + 1/11 - 1/14 + 1/14 - 1/15 + 1/15 - 1/28

1/7B= 1/2 - 1/28= 13/28

B= 13/28 : 1/7= 13/28.7= 13/4

Vậy B= 13/4

\(B=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{23.26}\)

\(B=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+....+\frac{1}{23}-\frac{1}{26}\)

\(B=\frac{1}{2}-\frac{1}{26}\)

\(B=\frac{13}{26}-\frac{1}{26}\)

\(B=\frac{12}{26}=\frac{4}{13}\)

Ta có: 3/2.5=3/3.(1/2-1/5)

3/5.8=3/3.(1/5-1/8)

3/8.11=3/3.(1/8-1/11)

...............................

3/23.26=3/3.(1/23-1/26)

Cộng từng vế ta đc:

B=3/3.(1/5-1/26)=1.21/130=21/130

B = 1/2 - 1/5 + 1/5 - 1/8 + 1/8 - ... - 1/26

B = 1/2 - 1/26

B = 6/13 nha bạn

E=\(\frac{5}{1.2}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)

E.\(\frac{1}{7}\)=\(\frac{5}{1.2.7}+\frac{4}{1.11.7}+\frac{3}{11.2.7}+\frac{1}{2.15.7}+\frac{13}{15.4.7}\)

E.\(\frac{1}{7}\)=\(\frac{5}{7.2}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\)

E.\(\frac{1}{7}\)=\(\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}\)

E.\(\frac{1}{7}\)=\(\frac{1}{2}-\frac{1}{28}\)

E.\(\frac{1}{7}=\frac{13}{28}\)

E=\(\frac{13}{28}:\frac{1}{7}=\frac{13}{4}\)

\(E=\frac{5}{1.2}+\frac{1}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)

\(E=\frac{5}{2}+\frac{1}{11}+\frac{3}{22}+\frac{1}{30}+\frac{13}{60}\)

\(E=\frac{5}{2}+\left(\frac{1}{11}+\frac{3}{22}\right)+\left(\frac{1}{30}+\frac{13}{60}\right)\)

\(E=\frac{5}{2}+\left(\frac{2}{22}+\frac{3}{22}\right)+\left(\frac{2}{60}+\frac{13}{60}\right)\)

\(E=\frac{5}{2}+\frac{5}{22}+\frac{15}{60}\)

\(E=\frac{55}{22}+\frac{5}{22}+\frac{1}{4}\)

\(E=\frac{60}{22}+\frac{1}{4}\)

\(E=\frac{30}{11}+\frac{1}{4}\)

\(E=\frac{120}{44}+\frac{11}{44}\)\(=\frac{131}{44}\)

k mình nha chúc bạn học giỏi