convergence
Problem-solving strategies for convergence in real analysis
Packaged view
This page reorganizes the original catalog entry around fit, installability, and workflow context first. The original raw source lives below.
Install command
npx @skill-hub/cli install parcadei-continuous-claude-v3-convergence
Repository
Skill path: .claude/skills/math/real-analysis/convergence
Problem-solving strategies for convergence in real analysis
Open repositoryBest for
Primary workflow: Ship Full Stack.
Technical facets: Full Stack.
Target audience: everyone.
License: Unknown.
Original source
Catalog source: SkillHub Club.
Repository owner: parcadei.
This is still a mirrored public skill entry. Review the repository before installing into production workflows.
What it helps with
- Install convergence into Claude Code, Codex CLI, Gemini CLI, or OpenCode workflows
- Review https://github.com/parcadei/Continuous-Claude-v3 before adding convergence to shared team environments
- Use convergence for development workflows
Works across
Favorites: 0.
Sub-skills: 0.
Aggregator: No.
Original source / Raw SKILL.md
---
name: convergence
description: "Problem-solving strategies for convergence in real analysis"
allowed-tools: [Bash, Read]
---
# 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 prove` for 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
```bash
uv run python -m runtime.harness scripts/sympy_compute.py limit "a_n" --var n --at oo
```
### Sympy_Sum
```bash
uv run python -m runtime.harness scripts/sympy_compute.py sum "1/n**2" --var n --from 1 --to oo
```
### Z3_Prove
```bash
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.