\(\frac{5^2}{6\cdot11}+\frac{5^2}{11\cdot16}+...+\frac{5^2}{91\cdot96}\)

\(=5\left(\frac{5}{6\cdot11}+\frac{5}{11\cdot16}+...+\frac{5}{91\cdot96}\right)\)

\(=5\left(\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{91}-\frac{1}{96}\right)\)

\(=5\left(\frac{1}{6}-\frac{1}{96}\right)\)\(=5\cdot\frac{5}{32}\)\(=\frac{25}{32}\)

chắc là tui có thể giúp đc đó

ta gọi biểu thức trên là A 

ta có :\(A=\frac{5^2}{6x11}+\frac{5^2}{11x16}+.........+\frac{5^2}{91x96}.\)

             \(=\frac{1}{5}\left(\frac{5}{6}-\frac{5}{11}\right)+\frac{1}{5}\left(\frac{5}{11}-\frac{5}{16}\right)+.........+\frac{1}{5}\left(\frac{5}{91}-\frac{5}{96}\right)\)

              \(=\frac{1}{5}\left(\frac{5}{6}-\frac{5}{11}+\frac{5}{11}-\frac{5}{16}+........+\frac{5}{91}-\frac{5}{96}\right)\)

               \(=\frac{1}{5}\left(\frac{5}{6}-\frac{5}{96}\right)\)

                 \(=\frac{1}{5}x\frac{25}{32}\)

                  \(=\frac{5}{32}\)

vậy biểu thức \(A=\frac{5}{32}\)

E=\(\frac{10}{1\cdot6}\) +\(\frac{10}{6\cdot11}\) +\(\frac{10}{11\cdot16}\) +\(\frac{10}{16\cdot21}\) +\(\frac{10}{21\cdot26}\) +\(\frac{10}{26\cdot31}\)                                                                                      =  5*(1-\(\frac{1}{31}\) )                                                                                                                                                                                 =5*\(\frac{30}{31}\)        =\(\frac{150}{31}\) 

S:5=\(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{21.26}\)

S:5=\(\frac{6-1}{1.6}+\frac{11-6}{6.11}+...+\frac{26-21}{21.26}\)

S:5=\(\frac{6}{1.6}-\frac{1}{1.6}+\frac{11}{6.11}-\frac{6}{6.11}+...+\frac{26}{21.26}-\frac{21}{21.26}\)

S:5=1-\(\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+....+\frac{1}{21}-\frac{1}{26}\)

S:5=1-\(\frac{1}{26}\)

S:5=\(\frac{25}{26}\)

S=\(\frac{25}{26}.5\)

S=\(\frac{125}{26}\)

\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}\)

= \(5\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}\right)\)

=\(5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}\right)\)=\(5\left(1-\frac{1}{26}\right)\)

=\(5.\frac{25}{26}\)

=\(\frac{125}{26}\)

Ta có:

\(A=\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+...+\frac{5^2}{26.31}\)

\(A=5\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right)\)

\(A=5\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)\)

\(A=5\left(\frac{1}{1}-\frac{1}{31}\right)\)

\(A=5.\frac{30}{31}\)

\(A=\frac{150}{31}\)

Vậy \(A=\frac{150}{31}\)

Ta có : \(\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+.....+\frac{5^2}{26.31}\)

\(=5\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+....+\frac{5}{26.31}\right)\)

\(=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+....+\frac{1}{26}-\frac{1}{31}\right)\)

\(=5\left(1-\frac{1}{31}\right)=5.\frac{30}{31}=\frac{150}{31}\)

\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}=5\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right)=5\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-...+\frac{1}{26}-\frac{1}{31}\right)\)

\(=5\left(1-\frac{1}{31}\right)=\frac{5.30}{31}=\frac{150}{31}\)

Ta có : 

\(S=\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}\)

\(S=5\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}\right)\)

\(S=5\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}\right)\)

\(S=5\left(1-\frac{1}{26}\right)\)

\(S=5.\frac{25}{26}\)

\(S=\frac{125}{26}\)

Vậy \(S=\frac{125}{26}\)

Chúc bạn học tốt ~ 

S=125/26

A=\(\frac{5^2}{1.6}\)+\(\frac{5^2}{6.11}\)+....+\(\frac{5^2}{26.31}\)=\(\frac{25}{1.6}\)+\(\frac{25}{6.11}\)+.....+\(\frac{25}{26.31}\)

\(\frac{1}{5}\)A=\(\frac{5}{1.6}\)+\(\frac{5}{6.11}\)+....+\(\frac{5}{26.31}\)=1-\(\frac{1}{6}\)+\(\frac{1}{6}\)-\(\frac{1}{11}\)+....+\(\frac{1}{26}\)-\(\frac{1}{31}\)=1-\(\frac{1}{31}\)=\(\frac{30}{31}\)

A=\(\frac{30}{31}\):\(\frac{1}{5}\)

A=\(\frac{150}{31}\)

150/31.

Tích cho mk nha.