convergence
Strategies and tools for testing mathematical convergence in real analysis.
Install
mkdir -p .claude/skills/convergence && curl -L -o skill.zip "https://agentskills.codes/api/skills/download/3321" && unzip -o skill.zip -d .claude/skills/convergence && rm skill.zipInstalls to .claude/skills/convergence
Activation
This is the description your AI agent reads to decide when to run this skill — the better it matches your request, the more reliably it fires.
Problem-solving strategies for convergence in real analysisKey capabilities
- →Identify sequence and series types
- →Apply ratio and root tests for convergence
- →Verify mathematical inequality bounds
- →Compute series sums for convergent sequences
How it works
It uses a decision tree to categorize series and applies Sympy for limit calculations and Z3 for proving inequality bounds.
Inputs & outputs
When to use convergence
- →Test series convergence
- →Verify mathematical bounds
- →Compute series sums
About this skill
Convergence
When to Use
Use this skill when working on convergence problems in real analysis.
Decision Tree
-
Identify Sequence/Series Type
- Geometric series: |r| < 1 converges
- p-series: p > 1 converges
- Alternating series: check decreasing + limit 0
-
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
- Ratio test:
-
Verify Bounds
- Use
z3_solve.py provefor inequality bounds - Check monotonicity with derivatives
- Use
-
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 oo
Sympy_Sum
uv run python -m runtime.harness scripts/sympy_compute.py sum "1/n**2" --var n --from 1 --to oo
Z3_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.
When not to use it
- →When the problem involves non-real analysis domains
- →When the series is divergent and no sum exists
Limitations
- →Limited to real analysis convergence problems
How it compares
This skill provides a programmatic decision tree and automated tool execution compared to manual algebraic derivation.
Compared to similar skills
convergence side by side with the closest alternatives in the catalog.
| Skill | Installs | Updated | Safety | Difficulty |
|---|---|---|---|---|
| convergence (this skill) | 1 | 7mo | Review | Intermediate |
| literature-review | 559 | 2mo | Review | Advanced |
| openalex-database | 48 | 7mo | Review | Intermediate |
| scientific-critical-thinking | 18 | 7mo | Review | Advanced |
Try saying
Example prompts that trigger this skill in your AI assistant.
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