Can we cover a unit square with $\dfrac1k \times \dfrac1{k+1}$ rectangles, where $k \in \mathbb{N}$?

(Note that the areas sum to $1$ since $\displaystyle \sum_{k \in \mathbb{N}}\dfrac1{k(k+1)} = 1$)

[Here][1] is an MO thread discussing some of the progress on this problem.


  [1]: http://mathoverflow.net/questions/34145/can-we-cover-the-unit-square-by-these-rectangles