Unit 12 Honors / Extended Practice

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Honors / Extended pathway

Convergence Tests & Conditional Behavior

Deeper proof, synthesis, parameter analysis, and unfamiliar applications.

1. Determine Σ1/(n²+3).

2. Which statement best describes the central reasoning in Direct Comparison Test?

3. Test Σ(3n+1)/(n³+2).

4. Which statement best describes the central reasoning in Limit Comparison Test?

5. Test Σ(−1)^{n+1}/n.

6. Which statement best describes the central reasoning in Alternating Series & Error Bounds?

7. Classify Σ(−1)^{n+1}/n.

8. Which statement best describes the central reasoning in Absolute vs Conditional Convergence?

9. Test Σ3^n/n!.

10. Which statement best describes the central reasoning in Ratio Test?

11. Test Σ[(2n+1)/(3n)]^n.

12. Which statement best describes the central reasoning in Root Test?

13. Why is the ratio test inconclusive for Σ1/n²?

14. Which statement best describes the central reasoning in Test Selection, Counterexamples & Decision Logic?

β Beta Program