Can we write $\displaystyle 1, \frac12, \frac13, \frac14, ...$ into the lattice points of the quarter plane that the followings are true:

- the sum of the numbers is 2 in each row

- the sum of the numbers is $\displaystyle \infty$ in each column

- there is a number in each cell

- each number is in one and only one cell

Thank you for any help!