EDB — 0D9

Exercises

1. [0D9]

   Let \(a_ k = \sqrt[3]{ k^ 3 + k} − k\). Prove that

   \[ ∑_{k=1}^ n a_ k ∼ \frac{1}{3} \log (n) \]

   that is, the ratio between the two above sequences tends to \(1\) when \(n → ∞\).

   Solution 1

   [0DB]↺↻