Determine the convergence of ∑n=1∞(1n−sin1n)\sum_{n=1}^{\infty} \left( \frac{1}{n} - \sin \frac{1}{n} \right)∑n=1∞(n1−sinn1).
Converges by Comparison Test with ∑1n3\sum \frac{1}{n^3}∑n31.
Diverges by Comparison Test with ∑1n\sum \frac{1}{n}∑n1.
Converges by Comparison Test with ∑1n2\sum \frac{1}{n^2}∑n21.
Diverges because terms do not approach 0.