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IBM

MCP Math Server

by IBM

harmonic_series

Calculate the nth partial sum of the harmonic series: 1 + 1/2 + 1/3 + ... + 1/n. Input an integer n to compute the sum of reciprocals up to that term.

Instructions

Calculate the nth partial sum of the harmonic series: 1 + 1/2 + 1/3 + ... + 1/n. (Domain: arithmetic, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
Behavior2/5

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

No annotations are provided, so the description carries full burden. It states the calculation but doesn't disclose behavioral traits like precision limits, handling of large n values, error conditions, or return format. For a computational tool with zero annotation coverage, this leaves significant gaps in understanding its operation.

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

Conciseness5/5

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

The description is appropriately sized and front-loaded, with the core purpose in the first sentence and domain/category tags efficiently appended. Every sentence earns its place without redundancy or unnecessary elaboration.

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

Completeness2/5

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

Given no annotations, 0% schema coverage, and no output schema, the description is incomplete. It covers the basic purpose but lacks details on behavior, parameter constraints, return values, and error handling, which are essential for a computational tool with one parameter.

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

Parameters3/5

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

Schema description coverage is 0%, so the description must compensate. It mentions 'n' as the parameter in the formula context, adding meaning beyond the schema's type declaration. However, it doesn't specify constraints (e.g., n must be positive integer) or provide examples, leaving some semantic gaps.

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

Purpose5/5

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

The description clearly states the tool's purpose with a specific verb ('calculate') and resource ('nth partial sum of the harmonic series'), including the mathematical formula. It distinguishes from siblings by specifying the harmonic series partial sum, unlike general arithmetic tools like 'arithmetic_series' or 'harmonic_number'.

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

Usage Guidelines3/5

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

The description implies usage for calculating harmonic series partial sums, with domain/category tags ('arithmetic', 'general') providing some context. However, it lacks explicit guidance on when to use this versus alternatives like 'harmonic_number' or 'harmonic_analysis', and doesn't mention prerequisites or exclusions.

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

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