# Last element in the world

Let $${ A }_{ 1776 }$$ be the set $$\left\{ \dfrac { 1 }{ 1 } ,\dfrac { 1 }{ 2 } ,\dfrac { 1 }{ 3 } ,\ldots ,\dfrac { 1 }{ 1775 } ,\dfrac { 1 }{ 1776 } \right\}$$.

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 last element?

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