The Basel Problem, named after the Swiss city of Basel, has troubled mathematicians for centuries. It involves finding the sum of the reciprocals of the squares of natural numbers. Euler successfully solved this, demonstrating that the sum is $\frac{\pi^2}{6}$. Later, he expanded his methods and knowledge to find closed-form solutions for sums of reciprocals of 4th, 6th, and other even powers. However, these methods did not lead to an exact solution for the sum of the reciprocals of cubes of natural numbers. The thesis addresses the resolution of these problems and explores Euler's attempt to evaluate the sum of the reciprocals of cubes by transforming it into a sum of a constant and an analytically intractable integral.
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