Fun with Former series Do you know the precise value of the summation of the reciprocals...
Fun with Former series Do you know the precise value of the summation of the reciprocals of the squares of the natural numbers. This is a famous problem in mathematical analysis with relevance to number theory. It was first posed by Pietro Mengoli in 164-1 and solved by Euler in 1735. Since the problem had withstood the attacks of the leading mathematicians of the day, Euler's solution brought him immediate fame when he was twenty-eight. Let's solve it using Fourier series (a tool that wasn't yet available to Euler!) Define the periodic function f(x) = x2 for and compute the Fourier series. Evaluate the function at x = pi and use the Fourier series to evaluate The answer is Your job is to show how this comes about!)