Euler's Pentagonal Numbers Theorem/Historical Note

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Historical Note on Euler's Pentagonal Numbers Theorem

This result was first noticed by Leonhard Paul Euler, who noticed the pattern on starting to multiply out the given infinite product, but he was initially unable to prove it except by a process of informal induction.

Despite this inability, he was so certain of the pattern that he used it as the basis of the development of further theorems.


Sources