Convergence When to Use Use this skill when working on convergence problems in real analysis. Decision Tree 1. Identify Sequence/Series Type - Geometric series: |r| < 1 converges - p-series: p 1 converges - Alternating series: check decreasing + limit 0 2. Apply Convergence Tests - Ratio test: - Root test: - Comparison test: find bounding series 3. Verify Bounds - Use for inequality bounds - Check monotonicity with derivatives 4. Compute Sum (if convergent) - Tool Commands Sympy Limit Sympy Sum Z3 Prove Cognitive Tools Reference See for full tool documentation. ---