Problem 300 (difficulty: 4/10)

Is it convergent?

\(\displaystyle \sqrt[n]{n^2+\cos n} \)

Solution:

\(\displaystyle 1< \sqrt[n]{n^2+\cos n}< \sqrt[n]{n^3}= \left(\sqrt[n]{n}\right)^3\to 1^3=1\).

Give me another random problem!