来源信息
- 仓库
- parcadei/Continuous-Claude-v3
- 最近来源活动
- 2026年1月10日 01:54
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SKILL.md
来源说明 · 只读预览- 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.
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