geometric_sum

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the infinite series capability for |r| < 1, which is useful context about the tool's behavior. However, it fails to describe critical aspects: whether it handles edge cases (e.g., r = 1, negative terms), what happens with invalid inputs (e.g., non-numeric values), the return format (e.g., number, error message), or performance considerations. For a mathematical tool with no annotation coverage, this leaves significant gaps in understanding how it behaves.

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?

The description is concise and front-loaded: the first sentence directly states the purpose. The second sentence adds useful context about infinite series, and the parenthetical note ('Domain: arithmetic, Category: general') is brief though not highly informative. There is no wasted text, and it efficiently conveys core information in two sentences.

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?

Given the complexity (a mathematical calculation tool with 3 parameters), no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It lacks details on parameter meanings, error handling, return values, and edge cases. While it hints at infinite series behavior, it doesn't provide enough context for reliable use, especially compared to well-documented siblings like 'arithmetic_sum' or 'geometric_sequence'.

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?

The input schema has 3 parameters with 0% description coverage, meaning the schema provides no semantic information. The description does not mention any parameters by name or explain their roles (e.g., 'first_term' as the initial value, 'common_ratio' as the multiplier, 'num_terms' as optional for finite sums). It only implies the use of a common ratio ('r') for infinite sums. With low schema coverage, the description fails to compensate adequately, leaving parameters largely undocumented.

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?

The description clearly states the tool's purpose: 'Calculate the sum of a geometric sequence.' It specifies the verb ('calculate') and resource ('sum of a geometric sequence'), and distinguishes it from siblings like 'geometric_sequence' (which generates terms) and 'geometric_series' (which might refer to series representation). However, it doesn't explicitly differentiate from 'series_sum' or 'power_series_sum', which could also compute sums, though those are more general.

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 description provides some implied usage context: it mentions 'For |r| < 1, can calculate infinite series sum,' which hints at when to use it for infinite vs. finite sums. However, it lacks explicit guidance on when to choose this tool over alternatives like 'arithmetic_sum' or 'series_sum', and doesn't specify prerequisites or exclusions (e.g., handling of divergent series). The mention of 'Domain: arithmetic, Category: general' is vague and doesn't offer practical usage rules.

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