MathDB
Is it convergent?

Source: IMS 2014 - Day2 - Problem8

October 4, 2014
trigonometryreal analysisreal analysis unsolved

Problem Statement

Is n=1+cosnn(1+12++1n)\sum_{n=1}^{+\infty}\frac{\cos n}{n}(1 + \frac{1}{\sqrt{2}} + \cdots + \frac{1}{\sqrt{n}}) convergent? why?