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Convergence

parcadei/convergence

Problem-solving strategies for convergence in real analysis

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on the repository, not the skill itself

Install

one command, takes just this skill from the repository 
npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill convergence

The instruction itself

8 sections, as written by the author

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

How to use it

Copy the folder

Take parcadei/convergence from the repository into ~/.claude/skills for personal use, or into .claude/skills inside a project.

Check the name does not clash

The agent identifies a skill by the name field in its header. Two skills with the same name cannot sit side by side — one of them will be ignored.