Two packing problems (Q1377835)

The author shows that the squares of sides \({1\over 3},{1\over 5},{1\over 7},{1\over 9},\dots\) can all be packed into a rectangle of size \({71\over 105}\) by \({15182\over 43407}\). Similarly, all the rectangles of size \({1\over n}\) by \({1\over n+1}\) \((n\geq 1)\) can be packed into the square of size \({501\over 500}\).