The American Mathematical Monthly 115(8)If f(x)=(πIxI) 2 on π,π, prove that f(x)=π 2 /3 Σ(4 cos nx/n 2) and deduce that Σ1/n 2 =π 2 /6 , Σ1/n 4 =π 4 /90 Note; Cos^2 π/6In today's blog, I show the proof that ∑ 1/n 2 = π 2 /6 For background on Basel's problem and Leonhard Euler's technique for arriving at the solution, see here In today's blog, I show a proof that Euler's solution is correct Most of the content in today's blog is taken from the Wikipedia article on the Basel Problem See references
Testing The Convergence Of Sum Limits N 1 Infty Frac N Pi N E N 2 Mathematics Stack Exchange