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Convergence — measured AI agent skill | DecimalAI

vibeeval/convergence

SkillScore95Maintained

Problem-solving strategies for convergence in real analysis

by vibeeval

Links this skill to your agents and keeps it current with the author’s updates.

Automatic

Tutoring & Education pack

decimalai skills pull vibeeval-convergence

Get this skill — curl · raw file

curl -fsSL https://app.decimal.ai/s/vibeeval-convergence/SKILL.md

Raw file: /s/vibeeval-convergence/SKILL.md ↗ · machine-readable summary at /s/vibeeval-convergence.json ↗

In productionGlobal

how this skill behaves on real traffic · last 30 days

No production data for this skill yet — usage numbers appear here once agents start running it.

Anonymized aggregate across every org using this skill — proof from real production use, not a demo.

Does this skill help? · Benchmark: with vs. withoutsign in to run this on your agents

22 test cases from the publisher’s eval.yaml · each run twice on gemini-3.6-flash — with the skill injected, then without · last run 6d ago

—-26% tokens0% turns95% of whole cases pass with skill (21/22)

Test case	Without → With	Effect	Δ tokens	Δ turns
case-04	✗→✓	▲ Improved	-18%	0%
case-07	✗→✓	▲ Improved	-70%	0%
case-08	✗→✓	▲ Improved	-58%	0%
case-09	✗→✓	▲ Improved	-39%	0%
case-11	✗→✓	▲ Improved	-68%	0%

Showing 5 of 22 cases

SkillSafety

✓ 3 of 3 passed

Code scan15 of 15 checks clean

0 critical · 0 warning · 0 info — scanner v4 — 8/1/2026

live_secretremote_code_executionreverse_shelldata_exfiltrationssrf_metadataagent_snoopinganti_refusaldestructive_commandsobfuscated_unicodeunicode_homoglyphopaque_blobsuspicious_urltool_overreachtrigger_abuseprompt_injection_phrasing

IntentSafe

LLM judge · does the skill do what it claims

ContentClean

LLM judge · policy & harmful-content review

Source

Imported

vibeeval / vibecosystem

skills/math/real-analysis/convergence/SKILL.md

View on GitHub ↗

License MITImported 8/1/2026Version v1

Skill contents

SKILL.md

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

bash
uv run python -m runtime.harness scripts/sympy_compute.py limit "a_n" --var n --at oo

Sympy_Sum

bash
uv run python -m runtime.harness scripts/sympy_compute.py sum "1/n**2" --var n --from 1 --to oo

Z3_Prove

bash
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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