{"uid":"cap_ilDzFZ06xpSYnkZueMnZV","slug":"numora-calculus-series-computation-0dbcf6e2","name":"Numora Calculus Series Computation","description":"100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.","url":"https://numormo.vercel.app/api/calculus/series","method":"POST","headers":{},"bodySchema":{"type":"object","required":["fn"],"properties":{"fn":{"type":"string","description":"Term expression with index n"},"maxTerms":{"type":"integer"},"tolerance":{"type":"number"}}},"responseSchema":{"type":"object","required":["success","result","computation"],"properties":{"result":{"type":"object","description":"Computation result varies by endpoint"},"success":{"type":"boolean","description":"Always true on success"},"computation":{"type":"string","description":"Human-readable description of what was computed"}}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.1","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"registry","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.1/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_J_Q0MAi8qzlIFDvyZsEFF","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.1","costPer":"request","priority":0,"asset":null,"unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes the sum or convergence of a mathematical series given a term expression in index n, with optional term limit and tolerance.","exampleAgentPrompt":"Can you compute the sum of the series whose nth term is 1/n^2, using up to 10000 terms and a tolerance of 0.0001?","exampleUseCases":[{"title":"Verify convergence of harmonic series","prompt":"I need to check numerically whether the series with nth term 1/n converges — can you sum it up to 5000 terms with a tolerance of 0.001 and tell me what you get?"},{"title":"Compute Taylor series approximation","prompt":"Sum the series whose nth term is (-1)^n / (2n+1) up to 1000 terms with tolerance 1e-6 — this should approximate pi/4."},{"title":"Financial perpetuity series valuation","prompt":"Compute the sum of the series where the nth term is 0.95^n, up to 500 terms with tolerance 0.0001, so I can estimate the present value of a geometric cash flow stream."}],"resultDescription":"Returns a JSON object with a boolean success flag, a result object containing the computed series sum and convergence details, and a human-readable computation string describing what was calculated.","failureModes":["Invalid or unparseable fn expression returns an error","Non-convergent series may exhaust maxTerms without reaching tolerance","Missing required fn parameter returns a 400-level error","Division by zero or undefined terms within the expression may cause computation failure","Very large maxTerms values may increase latency or timeout"],"whenToPreferThis":"Choose this endpoint when you need to numerically compute the sum or convergence behavior of a series defined by a closed-form nth-term expression, especially for calculus, financial math, or physics applications. Prefer it over general-purpose code execution when you want a fast, stateless, zero-dependency computation with micropayment pricing and no environment setup.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T00:32:02.999Z","isFirstParty":false}