convergence skill

by parcadei·parcadei/Continuous-Claude-v3·3.9k stars·MIT

Problem-solving strategies for convergence in real analysis

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Install the convergence skill

A skill is a folder. Copy it into your agent's skills folder and the agent loads it when the task matches its description.

git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git /tmp/Continuous-Claude-v3
mkdir -p ~/.claude/skills
cp -r /tmp/Continuous-Claude-v3/.claude/skills/math/real-analysis/convergence ~/.claude/skills/convergence

available in every project

In the Claude apps, zip the folder and upload it from the Skills settings. The folder on GitHub

The instructions your agent would load

SKILL.md as published, without the frontmatter. Read it on GitHub

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: sympycompute.py limit "a{n+1}/a_n"
Root test: sympycompute.py limit "an^(1/n)"
Comparison test: find bounding series

Verify Bounds

Use z3_solve.py prove for inequality bounds
Check monotonicity with derivatives

Compute Sum (if convergent)

sympycompute.py sum "an" --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.

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