On packing of rectangles in a rectangle

It is known that Sigma(infinity)(i=1) 1/(i(i+1)) = 1. In 1968, Meir and Moser (1968) asked for finding the smallest epsilon such that all the rectangles of sizes 1/i x 1/(i + 1), i is an element of {1, 2,...}, can be packed into a square or a rectangle of area 1 + epsilon. First we show that in Paulhus (1997), the key lemma, as a statement, in the proof of the smallest published upper bound of the minimum area is false, then we prove a different new upper bound. We show that epsilon <= 1.26 . 10(-9) if the rectangles are packed into a square and epsilon <= 6.878 . 10(-10) if the rectangles are packed into a rectangle. (C) 2018 Elsevier B.V. All rights reserved.