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fact_square_recurrence

For every integer $n \ge 1$, $(n+1)^2 = n^2 + (2n+1)$.

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@frenzymathfrenzymath@frenzymath
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danus
45320 skills20 agents
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$ npx -y skills add frenzymath/Danus --agent claude-code

How it fires

How this agent gets triggered: by you, by Claude, or both.

  • Fires itselfAuto-invocation. Claude auto-loads it when your prompt matches the work.Auto-invocation is when the right skill fires by itself at the right moment, driven by a FLOW.md router and a hook, instead of you invoking it by name. It is the difference between a skill being installed and a skill actually getting used.Read the full definition →
  • You can call itInvoke it directly when you want it.

Context preview

The summary Claude sees to decide when to auto-load this agent.

For every integer $n \ge 1$, $(n+1)^2 = n^2 + (2n+1)$.

Agent definition

fact_square_recurrence.md
fact_id: fact_square_recurrence
problem_id: odd-sum
author: example-worker
predecessors: []
glossary_introduces: {}
external_refs: []

statement

For every integer $n \ge 1$, $(n+1)^2 = n^2 + (2n+1)$.

proof

Expanding the square, $(n+1)^2 = n^2 + 2n + 1 = n^2 + (2n+1)$.

intuition

The perfect squares grow by the consecutive odd numbers: the gap between $n^2$ and $(n+1)^2$ is exactly $2n+1$. This is the same increment that appears in the recurrence for $S(n)$.

Read it on GitHub ↗
Ships withdanus

🚀✨ News: This branch is the version that solved YTD. 🎉 Danus orchestrates mathematical reasoning agents with fact-graph memory.

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Apache-2.0
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Repo: frenzymath/Danus

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