Abstract
In 1734, Leonhard Euler summed the infinite series of reciprocals of the squares, thereby solving a challenge known as the “Basel problem.” He later extended his method to find closed-form sums for the reciprocals of 4th, 6th, and other even powers. But those techniques did not yield a value for the sum of the reciprocals of the cubes. Here, we show how Euler tried to evaluate this series by transforming it into the sum of a strange constant and an even stranger integral.
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