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Leonhard Euler shows signs of genius at an early age in Switerland, where he is born in 1707. He begins publishing papers as a teen and is appointed by the Russian Czar to the Academy in St. Petersburg at the age of 20. He possesses a remarkable memory and is able to do complicated mathematical operations in his head. Over the course of his life, he produces an incredible amount of work despite his increasing blindness. He dies suddenly in 1783, working on mathematics up until his death.

Euler would certainly have encountered the series 1 + 1/4 + 1/9 + 1/16 ... + 1/k² ... from his teacher Johann Bernoulli, Dunham writes, and he sets out to find its sum. He begins by simply adding up the first several terms hoping to find a familiar number. This method does not produce a recognizable result. Using a method that involves both trigonometry and basic algebra, which...

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This section contains 281 words(approx. 1 page at 400 words per page) |