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smithery/parcadei

convergence

Problem-solving strategies for convergence in real analysis

Installation

$ npx skills add smithery/parcadei --skill convergence
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npx skills add smithery/parcadei
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More details

Agent compatibility

Declared targets from SKILL.md / docs. Unmarked agents are not listed — the skill may still install via the CLI.

Claude Code Declared
Cursor Not declared
Codex Not declared
GitHub Copilot Not declared
Windsurf Not declared
Gemini CLI Not declared
Cline Not declared
OpenCode Not declared

Skill metadata

Parsed from SKILL.md frontmatter.

Allowed toolsBash, Read
Declared agents claude-code

Package contents

Files included with this skill beyond the listing page.

  • skill md SKILL.md 1,264 B
  • docs SUMMARY.md 78 B

History

  1. First recorded snapshot · 0 installs

SKILL.md

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

  1. Apply Convergence Tests

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

  1. Verify Bounds

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

  1. 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.