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Problems > High School Math > 2003

Strange Sum

Let A1776 be the set { 1, 1/2, 1/3, ..., 1/1776 }

 

Remove any two elements, say a and b, from A1776, and replace them with the single number ab+a+b to form set A1775.
Continue in this manner, until you have performed 1775 such operations, to form set A1, which contains a single element.

 

 

What is this element?

 

 

Prove it!

 



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A Little Number Theory to Begin the School Year

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