EDB — 23F

Exercises

1. [23F](Proposed on 2022-12-13) Note:Written exam 29th January 2021.Let it be \(𝛼{\gt}0\). Say (justifying) for which \(𝛼\) the following series converge or diverge

   • \[ ∑_{n=1}^∞ \left({\sqrt[4]{n^ 8+n^𝛼} - n^ 2 }\right) \]
   • \[ ∑_{n=2}^∞ \left( \frac{1}{n^𝛼} - \frac{1}{n^𝛼+1} \right) \]
   • \[ ∑_{n=2}^∞ \frac{1}{(\log _ 2 n) ^{𝛼\log _ 2(n)}} \]

     where the logarithms are in base 2.

   Solution 1

   [23G]↺↻