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sum of products of 2, 4, 6, ..., 2000 of elements of {1/2, ..., 1/2001}

Source: Estonia IMO TST 2001 p4

March 26, 2020
SumProductalgebracombinatorics

Problem Statement

Consider all products by 2,4,6,...,20002, 4, 6, ..., 2000 of the elements of the set A={12,13,14,...,12000,12001}A =\left\{\frac12, \frac13, \frac14,...,\frac{1}{2000},\frac{1}{2001}\right\} . Find the sum of all these products.
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