Euler was 28 years old when he proved that it converged.
The Basel Problem is also known as the Riemann Zeta function: ζ(2).
He studied the zeroes of the function sin x,
i.e. sin x= 0 for
sin x can be factorized as :
Note 1: On the right-hand side, any factor = 0 when
Right-hand side also -> 1 when x -> 0.
From Taylor series,
Product = Sum
Let’s expand the product, then compare the coefficient of the term
The coefficient for the term is (a + b + c + d +…)
“The Math Girls“