SHMARQL

harmonic series

<http://www.wikidata.org/entity/Q464100>

infinite series of the reciprocals of the positive integers
harmonic series
rdfs:label
"harmonic series"@en
skos:altLabel
"1 + ½ + ⅓ + …"@en
"1/1 + 1/2 + 1/3 + …"@en
"harmonic series (mathematics)"@en
schema:description
"infinite series of the reciprocals of the positive integers"@en
schema:dateModified "2026-11-08T22:45:43+00:00"^^xsd:dateTime
schema:version 2566759152
wikibase:identifiers 18
wikibase:sitelinks 50
wikibase:statements 32
p:P10376 wd:statement/Q464100-42a512ef-4610-54b2-b25c-720f94257504
wd:statement/Q464100-4babf1b2-46a3-d962-3970-0deb88dc5c67
wd:statement/Q464100-7d315b49-4b97-9c2f-8e3f-4fad15ada025
p:P10969 wd:statement/Q464100-16f63312-4df5-7a77-b364-65f94abdbcae
p:P11514 wd:statement/Q464100-CF9A88C9-3236-44FE-B54C-614E227DCF5B
p:P1343 wd:statement/Q464100-80976464-53DA-4D34-A1C0-2F8C4025F0A3
wd:statement/Q464100-D785746B-4149-4943-AF66-1BA079EE1C41
wd:statement/Q464100-ad3ab9b9-93e9-41da-8f67-e2411c56d233
wd:statement/Q464100-f8ac1f29-336b-4d7d-838f-edcc3196b13c
p:P18 wd:statement/Q464100-9a57d41d-42b9-84d9-702d-7a8ca6f1a104
p:P1889 wd:statement/Q464100-161946C3-D282-4E05-853A-EE8F06DE6C68
wd:statement/Q464100-a4418400-4687-c5d0-2fc9-44ab3379268a
p:P2534 wd:statement/Q464100-c23d8fd4-430e-0873-b819-088ef87615a4
p:P2812 wd:statement/Q464100-09D67EC2-7273-4222-8859-67347E437296
p:P2924 wd:statement/Q464100-420C9B48-9724-4B56-A942-481B906E935C
p:P31 wd:statement/Q464100-1acafd69-4a07-22ff-efb9-a11eb0d7f2b5
p:P3222 wd:statement/Q464100-E80FB0A2-854D-4F35-A064-3AF5B46D3EB1
p:P373 wd:statement/Q464100-0f1e3a29-7899-486c-924e-44d9258f17f6
p:P4342 wd:statement/Q464100-5A331CDC-E56F-48E5-AF1D-0796546A416A
p:P5019 wd:statement/Q464100-47BE1E56-4E1D-4C9A-8370-4D52C4E6CB78
p:P508 wd:statement/q464100-616B885C-73D7-4CF6-8FF5-6195468E2B72
p:P6104 wd:statement/Q464100-B03880C2-6ED4-4581-8E9D-755CFEC59854
p:P6366 wd:statement/Q464100-612BAC5A-D40B-47A0-8E70-2E909AE5C45C
p:P646 wd:statement/Q464100-5DE669F6-5DE1-4E46-A8AD-6B81D89C1FF3
p:P6781 wd:statement/Q464100-5ec174f8-4ccb-90de-a8cc-18cd3b661bbc
p:P7235 wd:statement/Q464100-2988f6a5-4bb5-774c-768c-fb3974a43336
wd:statement/Q464100-40a9e8d6-4a66-f3dd-39ac-402b0fe62c4d
p:P7554 wd:statement/Q464100-586F772E-3BE2-49F9-BD14-1AE348F7D1A4
wd:statement/Q464100-acb226f8-455c-d36e-2c7c-98e1cee1ffc0
p:P7726 wd:statement/Q464100-85c4c4b9-4c83-ae93-6bea-3eb65e310fef
p:P8313 wd:statement/Q464100-C5CD76D3-2BAE-4400-B435-FCB477D7BC6B
p:P9621 wd:statement/Q464100-71f32f94-4502-52bd-8c1c-d8f07f15a118
p:direct-normalized/P508 <http://purl.org/bncf/tid/22081>
p:direct-normalized/P6366 <https://makg.org/entity/68199440>
wdt:P10376 "computer-science/harmonic-series"
"engineering/harmonic-series"
"mathematics/harmonic-series"
wdt:P10969 "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="true" scriptlevel="0"><munderover><mo stretchy="false">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">=</mo><mn>0</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">&#x221E;</mi></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></mfrac></mrow><mo stretchy="false">=</mo><mn>1</mn><mo stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></mfrac></mrow><mo stretchy="false">+</mo><mo stretchy="false">&#x22EF;</mo><mo stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></mfrac></mrow><mo stretchy="false">+</mo><mo stretchy="false">&#x22EF;</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P11514 "garmonicheskii-riad-d5681b"
wdt:P1343 Armenian Soviet Encyclopedia, vol. 6
Mathwords
Great Soviet Encyclopedia (1926–1947)
Khan Academy
wdt:P18 <http://commons.wikimedia.org/wiki/Special:FilePath/HarmonicPartialSums.svg>
wdt:P1889 harmonic series
alternating harmonic series
wdt:P2534 "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="true" scriptlevel="0"><munderover><mo stretchy="false">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">&#x221E;</mi></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></mfrac></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P2812 "HarmonicSeries"
wdt:P31 series diverging to infinity
wdt:P3222 "harmonisk-serie"
wdt:P373 "Harmonic series (mathematics)"
wdt:P4342 "den_harmoniske_rekke"
wdt:P5019 "harmonische-folge"
wdt:P508 "22081"
wdt:P6104 WikiProject Mathematics
wdt:P6366 "68199440"
wdt:P646 "/m/011yyc"
wdt:P6781 "Definition:Harmonic_Series"
wdt:P7235 "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>n</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mo stretchy="false">&#x2211;</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P7554 "Harmonic_Series"
"Harmonic_series"
wdt:P7726 "HarmonicSeries"
wdt:P8313 "harmonisk_række"
wdt:P9621 "serie-armonica"
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