## Strange Sum

Let A_{1776} be the set { 1, ^{1}/_{2}, ^{1}/_{3}, ..., ^{1}/_{1776} }

Remove any two elements, say a and b, from A_{1776}, and replace them with the single number ab+a+b to form set A_{1775}.

Continue in this manner, until you have performed 1775 such operations, to form set A_{1}, which contains a single element.

What is this element?

Prove it!

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