Convergence
- 1 installs
- 3.9k repo stars
- Updated January 26, 2026
- parcadei/continuous-claude-v3
Guides Claude through real-analysis convergence problems using ratio, root, and comparison tests, then computing sums via sympy.
About
A decision-tree skill for testing sequence and series convergence with ratio, root, and comparison tests. A developer uses it when they want Claude to classify series and compute sums with sympy.
- Ratio, root, and comparison convergence tests
- Sum computation for convergent series with sympy
Convergence by the numbers
- 1 all-time installs (skills.sh)
- Ranked #1,803 of 2,064 Data Science & ML skills by installs in the Skillselion catalog
- Data as of Aug 5, 2026 (Skillselion catalog sync)
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| Installs | 1 |
|---|---|
| repo stars | ★ 3.9k |
| Last updated | January 26, 2026 |
| Repository | parcadei/continuous-claude-v3 ↗ |
What it does
Guides Claude through real-analysis convergence problems using ratio, root, and comparison tests, then computing sums via sympy.
Files
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:
sympy_compute.py limit "a_{n+1}/a_n" - Root test:
sympy_compute.py limit "a_n^(1/n)" - Comparison test: find bounding series
3. Verify Bounds
- Use
z3_solve.py provefor inequality bounds - Check monotonicity with derivatives
4. Compute Sum (if convergent)
sympy_compute.py sum "a_n" --var n --from 0 --to oo
Tool Commands
Sympy_Limit
uv run python -m runtime.harness scripts/sympy_compute.py limit "a_n" --var n --at ooSympy_Sum
uv run python -m runtime.harness scripts/sympy_compute.py sum "1/n**2" --var n --from 1 --to ooZ3_Prove
uv run python -m runtime.harness scripts/z3_solve.py prove "series_bounded"Cognitive Tools Reference
See .claude/skills/math-mode/SKILL.md for full tool documentation.
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