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

With no annotations, the description carries the full behavioral burden, and it discloses almost nothing: it does not say what happens for divergent series (|ratio| >= 1), what the return value looks like, or precision behavior. The one genuine addition is the cost/auth signal ("5 free trial calls per signed wallet"), which is useful but is the only behavioral fact provided.

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 definition is short and front-loaded, but the second sentence is a grammatically incomplete fragment ("Sum of infinite geometric") that adds no information beyond the title. The free-trial sentence is compact and useful.

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?

A three-parameter math tool with no annotations, no output schema, no parameter descriptions, and no sibling differentiation is left almost entirely unexplained. An agent cannot reliably determine which argument to supply, whether convergence matters, or what the tool returns.

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?

All three parameters (a, first, ratio) are undocumented at 0% schema coverage, and the description provides no clarification. "Geometric" weakly hints that ratio is the common ratio and that a/first are the first term, but the ambiguity between "a" and "first" is left entirely unaddressed, as are types and required-vs-optional status.

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 names the operation ("Infinite Geometric Sum") but not in a way that distinguishes it from close siblings such as x402-geometric-series-sum, x402-geometric-series, or x402-power-series. The second sentence ("Sum of infinite geometric") is a truncated restatement rather than added specificity about formula or convergence conditions.

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?

No when-to-use guidance is given, no distinction from the several near-identical geometric-series siblings, and no note about prerequisites such as |ratio| < 1. The only usage-adjacent text is a payment/trial note, which does not help an agent choose the tool.

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