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A Brief Introduction to Riemann Summation

 

According to legend, in school, a young Bernhard Riemann was assigned the daunting task of adding a series of integers that increment up by one to a hundred.  (i.e. 1+2+3+...+97+98+99+100)  

 

His teacher thought this ought to keep the students occupied for a while until, five minutes later, Bernhard showed his teacher the correct answer of 5050.

 

Here's how he did it...