Determine the convergence of ∑n=1∞(n2+1n−1)\sum_{n=1}^{\infty} (\sqrt[n]{n^2+1} - 1)∑n=1∞(nn2+1−1).
Converges because the terms approach 0.
Diverges by comparison with ∑lnnn\sum \frac{\ln n}{n}∑nlnn.
Converges by the Root Test.
Diverges by the Limit Comparison Test with ∑1n\sum \frac{1}{n}∑n1.