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 it discloses nothing: not whether the result is a numeric scalar, how divergence (|ratio| >= 1) is handled, or what errors can occur. The agent learns nothing about behavior beyond the name.

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 single sentence is short, but this is under-specification rather than conciseness. It wastes its one sentence repeating the tool title instead of front-loading the parameter meaning and convergence constraint.

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 computational tool with no annotations and no output schema requires the description to explain inputs, valid ranges, and result shape. None of that is present, leaving the definition completely inadequate for correct invocation.

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?

Coverage is technically 100%, but the schema descriptions are tautological placeholders ("A to process", "First to process", "Ratio to process") that convey no meaning for cryptic parameter names like 'a' and 'first'. The description does not compensate by mapping these to mathematical terms (first term, common ratio), so an agent still cannot reliably supply correct values.

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?

"Infinite Geometric Sum: Sum of infinite geometric" essentially restates the tool name/title rather than describing the operation. It does hint at the domain (infinite geometric series), but gives no verb, no statement of what is actually returned, and does not distinguish itself from close siblings like x402-geometric-series, x402-geometric-series-sum, or x402-arithmetic-series-sum.

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?

There is no indication of when to use this tool versus the many sibling series tools, no prerequisites, and no exclusions. The description also omits the crucial convergence condition (|ratio| < 1) that determines whether the tool is even applicable.

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