1. **State the problem:** Determine the convergence of the series $$\sum_{n=2}^\infty \frac{\sin(n+1) + \cos n}{n^2 - n}$$. 2. **Rewrite the general term:** The term is $$a_n = \frac{\sin(n+1) + \cos n}{n^2 - n}$$. 3. **Analyze the denominator:** Factor the denominator: $$n^2 - n = n(n-1)$$. 4. **Consider the behavior of numerator:** Since $$\sin(n+1)$$ and $$\cos n$$ are bounded between -1 and 1, the numerator is bounded: $$|\sin(n+1) + \cos n| \leq |\sin(n+1)| + |\cos n| \leq 2$$. 5. **Compare with a known convergent series:** Since $$|a_n| \leq \frac{2}{n(n-1)}$$ and for large $$n$$, $$n(n-1) \sim n^2$$, compare with $$\sum \frac{1}{n^2}$$ which converges (p-series with $$p=2>1$$). 6. **Use the Comparison Test:** Because $$\sum \frac{1}{n^2}$$ converges and $$|a_n| \leq \frac{2}{n(n-1)}$$ which behaves like $$\frac{2}{n^2}$$, the given series converges absolutely. 7. **Conclusion:** The series $$\sum_{n=2}^\infty \frac{\sin(n+1) + \cos n}{n^2 - n}$$ converges absolutely.