4. Let q> 0 be a real constant. Instead of using square boxes as in Question 3, imagine boxes in the shape of rectangles, where box n has base width 1/n and height 1/n. (Treat Question 3 as the special case q = 1.) (a) Imagine packing these new rectangular boxes according to the process detailed in Question 3. The picture from 3(a) won't change much, so do nothing here. (b) Upgrade your formula from 3(b) to find the interval [an, bn] supporting box number 2". The result should apply for any n 0 and any q> 0. (c) Adapt your work in 3(c) to apply with a general q>0. In particular, show that the height-limit of 1 remains correct. (d) Express as a series the total width of shelf required to hold all the boxes. Then determine which values of q>0 correspond to a finite total width. (e) The box-packing discussion above proves convergence for a certain family of series. Identify this family and make intelligent remarks that relate your findings here with important results discussed in class.