Question

`2/6+2/66+2/176+....+2/((5n−4).(5n+1))`

Answer 1

`2/6 + 2/66 + 2/176 + ...+ 2/((5n - 4)(5n + 1))`

`= 2(1/6+ 1/66 + 1/176 + ...+ 1/((5n - 4)(5n+1))`

`= 2(1/(1 . 6) + 1/(6 . 11) + 1/(11 . 16) + ... + 1/(5n-4)(5n+1))`

`= 2(1-1/6+1/6-1/11+....-1/(5n-4)+1/(5n-4) - 1/(5n+1))`

`= 2(1-1/(5n+1))`

`= 2/5 . (5n)/(5n+1)`

`= (2n)/(5n+1)`

Answer 2

Sửa: Dấu `=` thứ `2` thành `= 2(1/(1 . 6)+ 1/(6 . 11) + 1/(11 . 16) + ... + 1/((5n-4)(5n+1)))`