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Convergence

Skill parcadei/Continuous-Claude-v3/.claude/skills/math/real-analysis/convergence

Problem-solving strategies for convergence in real analysisFrom its SKILL.md

Install
npx -y skills add parcadei/Continuous-Claude-v3 --skill convergence

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SKILL.md

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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

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.

What ships with it

Read from the repository

Just SKILL.md. No reference files, no scripts.

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