The proof we provide above is the original proof of Euler, which assumes that one can express infinite polynomials(series) as product of their roots. 100 years later, Weierstrass proved his factorization theorem, which made Euler's proof valid. You can find several proofs of this infinite sum in the marvelous book 'Proofs from the Book'. https://www.patreon.com/pisagormath https://www.facebook.com/pisagor/ https://www.instagram.com/pisagormath/ https://twitter.com/PisagorMath