Determine the convergence of the series ∑n=1∞(n2+1−n)\sum_{n=1}^{\infty} \left( \sqrt{n^2 + 1} - n \right)∑n=1∞(n2+1−n).
Converges by Comparison Test with ∑1n\sum \frac{1}{n}∑n1
Diverges by Comparison Test with ∑12n\sum \frac{1}{2n}∑2n1
Converges by the Root Test
Diverges by the Ratio Test