@prefix dcterms: <http://purl.org/dc/terms/> .
@prefix edu: <https://knobit.org/def/> .
@prefix knobit: <https://knobit.org/id/knobit/> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix register: <https://knobit.org/id/register/> .
@prefix schema: <https://schema.org/> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .

knobit:K12-5214 a edu:Knobit ;
    rdfs:label "Derives the formula for the sum of a decreasing geometric sequence"@en,
        "Tuletab hääbuva geomeetrilise jada summa valemi"@et ;
    dcterms:identifier "K12-5214" ;
    dcterms:license <https://creativecommons.org/licenses/by/4.0/> ;
    dcterms:source "National Curriculum for Upper Secondary Schools, Annex 5, extended mathematics, course VII “Functions. Sequences”, learning outcome 6"@en,
        "GRÕK lisa 5, lai matemaatika, VII kursus „Funktsioonid. Arvjadad“, õpitulemus 6"@et ;
    skos:definition "Derives the sum formula as the limit of the sum of a geometric sequence when |q| < 1."@en,
        "Tuletab summavalemi geomeetrilise jada summa piirväärtusena, kui |q| < 1."@et ;
    skos:prefLabel "Derives the formula for the sum of a decreasing geometric sequence"@en,
        "Tuletab hääbuva geomeetrilise jada summa valemi"@et ;
    edu:actionVerb "Derives"@en,
        "Tuletab"@et ;
    edu:appliesKnowledge knobit:K12-5208 ;
    edu:assessmentCriterion "The derivation is correct: as n → ∞, qⁿ → 0 and S = b₁/(1 − q)"@en,
        "Tuletus on õige: n → ∞ korral qⁿ → 0 ja S = b₁/(1 − q)"@et ;
    edu:assessmentMethod "Practical task"@en,
        "Praktiline ülesanne"@et ;
    edu:contextFunction <https://knobit.org/def/contextFunction/actionExecution> ;
    edu:creationMethod <https://knobit.org/def/creationMethod/aiGenerated> ;
    edu:dependsOnKnobit knobit:K12-5213 ;
    edu:expectedResult "A justified derivation and the sum"@en,
        "Põhjendatud tuletus ja summa"@et ;
    edu:graphRelevance <https://knobit.org/def/graphRelevance/learnerState>,
        <https://knobit.org/def/graphRelevance/learningPath>,
        <https://knobit.org/def/graphRelevance/outcomeContent>,
        <https://knobit.org/def/graphRelevance/taskSelection> ;
    edu:knobitType <https://knobit.org/def/knobitType/skill> ;
    edu:targetObject "the derivation of the formula for the sum of a decreasing geometric sequence"@en,
        "hääbuva geomeetrilise jada summa valemi tuletus"@et ;
    schema:creativeWorkStatus "accepted" ;
    schema:isPartOf register:K12-SCOPE-1,
        register:K12-SCOPE-5000 .

edu:Knobit rdfs:label "Knobit"@en,
        "Knobit"@et .

knobit:K12-5208 rdfs:label "Explains the concept of a decreasing geometric sequence"@en,
        "Selgitab hääbuva geomeetrilise jada mõistet"@et .

knobit:K12-5213 rdfs:label "Derives the formula for the sum of the first n terms of a geometric sequence"@en,
        "Tuletab geomeetrilise jada n esimese liikme summa valemi"@et .