Yes, Euler demonstrated, as G. Pólya illustratively illuminates in his:

" Induction and Analogy in Mathematics; Vol. 1 of [Mathematics and Plausible Reasoning](https://en.wikipedia.org/wiki/Mathematics_and_plausible_reasoning)". 

Pólya gives an English translation of Euler's writing in [Ch. 6](https://books.google.com/books?id=-TWTcSa19jkC&pg=PA90).

 It can be read with very little prior knowledge.