Mechanics Marathon 4 - Piles of books

N N books of equal mass each of 1 m 1m are stacked in such a way that each of the book protudes above the one below it thus forming an arch.

Find the sum of the reciprocals of the lengths of each of the overhanging parts such that total length of the overhanging part is maximised.

n 2 n^2 N ( N 1 ) N(N-1) ( N 1 ) 2 (N-1)^2 ( N 1 ) ( n 2 ) (N-1)(n-2)

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