EDB — 1BX

Exercises

1. [1BX] Let’s go back to the exercise [0FP]↺↻: computing the Cauchy product of the series \(∑_{n=1}^∞ \frac{(-1)^{n-1}}{\sqrt{n}}\) with itself, produces the series \(∑_ n (-1)^ n c_ n\) with \(c_ n = ∑_{k=1}^{n-1} \frac 1{\sqrt{k(n-k)}}\); show that \(c_ n→ 𝜋\).

   Solution 1

   [1BY]↺↻