We have:

\(1+\dfrac{1+2}{2}+\dfrac{1+2+3}{3}+...+\dfrac{1+2+3+...+199}{199}\)

\(=1+\dfrac{2\cdot3:2}{2}+\dfrac{3\cdot4:2}{2}+...+\dfrac{199\cdot200:2}{199}\)

\(=1+\dfrac{3}{2}+\dfrac{4}{2}+\dfrac{5}{2}+...+\dfrac{200}{2}\)

\(=\dfrac{2}{2}+\dfrac{3}{2}+\dfrac{4}{2}+...+\dfrac{200}{2}\)\(=\dfrac{2+3+4+5+...+200}{2}=\dfrac{\left[\left(200-2+1\right):2\right]\left(2+200\right)}{2}=\dfrac{\dfrac{199}{2}\cdot202}{2}=\dfrac{20099}{2}\)

Answer of Dao Trong Luan must be    to ​ ​​ ​.

Answer of Dao Trong Luan must be  \(\dfrac{3.4:2}{2}\)  to ​ ​​ ​\(\dfrac{3.4:2}{3}\).