Câu hỏi 130
Tìm phân số lớn nhất trong 1010 phân số cho dưới đây:
$$
\frac{1}{2019},\quad \frac{1+2018}{2019+2},\quad \frac{1+2018+3}{2019+2+2017},\quad \frac{1+2018+3+2016}{2019+2+2017+4},\quad \frac{1+2018+3+2016+5}{2019+2+2017+4+2015},\quad \dots,
$$
$$
\frac{1+2018+3+2016+\dots+1009}{2019+2+2017+4+\dots+1011},\quad \frac{1+2018+3+2016+\dots+1009+1010}{2019+2+2017+4+\dots+1011+1010}.
$$
(Bohdan Rublyov)
$$
\frac{1}{2019},\quad \frac{1+2018}{2019+2},\quad \frac{1+2018+3}{2019+2+2017},\quad \frac{1+2018+3+2016}{2019+2+2017+4},\quad \frac{1+2018+3+2016+5}{2019+2+2017+4+2015},\quad \dots,
$$
$$
\frac{1+2018+3+2016+\dots+1009}{2019+2+2017+4+\dots+1011},\quad \frac{1+2018+3+2016+\dots+1009+1010}{2019+2+2017+4+\dots+1011+1010}.
$$
(Bohdan Rublyov)