4

Part of 2001 Estonia Team Selection Test

Problems(1)

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

Source: Estonia IMO TST 2001 p4

Consider all products by

2, 4, 6, ..., 2000

of the elements of the set

A =\left\{\frac12, \frac13, \frac14,...,\frac{1}{2000},\frac{1}{2001}\right\}

. Find the sum of all these products.

SumProductalgebracombinatorics