geometric_series

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries the full behavioral burden and does not meet it. It does not disclose what happens for divergent infinite series (|r| >= 1), whether n is ignored when summing infinitely, or what the response contains. For a math tool with no annotations and no output schema, this is a significant gap.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

A single efficient sentence that front-loads the verb and scope and packs the series formula inline. No waste.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With 3 required parameters, full schema coverage, no annotations, and no output schema, the description is minimally adequate. It omits the divergent/infinite-case behavior and edge conditions (n bounds, |r| threshold), which an agent would need to call the tool reliably.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100%, and each parameter (a=first term, r=common ratio, n=number of terms 1-1000) is documented in the schema. The description adds the series formula but no parameter syntax or format details beyond the schema, so the baseline 3 applies.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb (Calculate) and resource (finite and infinite sums of a geometric series), and even spells out the series form 'a, ar, ar^2, ...'. This is unambiguous and distinguishes it from siblings like harmonic_series or fibonacci_sequence.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

The mention of 'finite and infinite sums' implies the n parameter governs which mode applies, but the description never states when to use finite vs infinite, nor how n behaves for the infinite case (e.g., whether n is ignored when |r|<1). Usage is implied rather than stated.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.