EDB — 0FX

Exercises

1. [0FX]Prerequisites:[09N]↺↻.Note:From the written exam of March 27, 2010..Say for which \(𝛼∈ℝ\) the series

   \[ ∑_{(m,n)∈{\mathbb N}^ 2}\frac{1}{(n+m+1)^𝛼}\quad . \]

   converges. Then discuss, for \(N≥ 3\), the convergence of

   \[ ∑_{(m_ 1,\ldots m_ N)∈{\mathbb N}^ N}\frac{1}{(1+m_ 1+\ldots + m_ N)^𝛼}\quad . \]
   Solution 1

   [0FY]↺↻