Question

5²/6.11 + 5²/11.16 + ............+ 5²/91.96

Answer 1

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

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

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

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

Answer 2

chắc là tui có thể giúp đc đó

Answer 3

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 \(A=\frac{5}{32}\)

Answer 4

= 5² . ( \(\frac{5^2}{6}\): \(\frac{5^2}{11}\)+  \(\frac{5^2}{11}\) : \(\frac{5^2}{16}\)+ .... + \(\frac{5^2}{91}\):  \(\frac{5^2}{96}\))

= 5^{2 ( \(\frac{5^2}{6}\):  \(\frac{5^2}{96}\)})

= 5² . 16 

= 400