Best use case
convergence is best used when you need a repeatable AI agent workflow instead of a one-off prompt.
Problem-solving strategies for convergence in real analysis
Teams using convergence should expect a more consistent output, faster repeated execution, less prompt rewriting.
When to use this skill
- You want a reusable workflow that can be run more than once with consistent structure.
When not to use this skill
- You only need a quick one-off answer and do not need a reusable workflow.
- You cannot install or maintain the underlying files, dependencies, or repository context.
Installation
Claude Code / Cursor / Codex
Manual Installation
- Download SKILL.md from GitHub
- Place it in
.claude/skills/convergence/SKILL.mdinside your project - Restart your AI agent — it will auto-discover the skill
How convergence Compares
| Feature / Agent | convergence | Standard Approach |
|---|---|---|
| Platform Support | Not specified | Limited / Varies |
| Context Awareness | High | Baseline |
| Installation Complexity | Unknown | N/A |
Frequently Asked Questions
What does this skill do?
Problem-solving strategies for convergence in real analysis
Where can I find the source code?
You can find the source code on GitHub using the link provided at the top of the page.
SKILL.md Source
# 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"
```
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