Sum

The sum of two numbers is their value added together. This operation is called additive summation or addition. There are many ways of writing sums, including:

Addition ( $2+4+6=12$ )
Summation ( $\sum _{k=1}^{3}k=1+2+3=6$ )
Code:

Sum = 0

For I = M to N

Sum = Sum + X(I)

Next I (in Visual BASIC)

Sigma notation

Sigma notation is a mathematical notation to write long sums in a short way. Sigma notation uses the Greek letter Sigma ( $\Sigma$ ), and takes upper and lower bounds which tell us where the sum begins and where it ends. The lower bound usually has a variable (called the index, often denoted by $i$ , $j$ or $k$ ^[1]) along with a value, such as " $i=2$ ". This tells us that the summation begins at 2, and goes up by 1 until it reaches the number on the top.^[2]

Properties

\sum _{i=1}^{n}0=0

\sum _{i=1}^{n}1=n

\sum _{i=1}^{n}n=n^{2}

\sum _{i=1}^{n}i={\frac {n(n+1)}{2}}

^[3]

\sum _{i=1}^{n}i^{2}={\frac {n(n+1)(2n+1)}{6}}

^[3]

\sum _{i=1}^{n}i^{3}={\frac {n^{2}(n+1)^{2}}{4}}

^[3]

\sum _{i=1}^{\infty }a_{i}=\lim _{t\to \infty }\sum _{i=1}^{t}a_{i}

Applications

Sums are used to represent series and sequences. For example:

\sum _{i=1}^{4}{\frac {1}{2^{i}}}={\frac {1}{2^{1}}}+{\frac {1}{2^{2}}}+{\frac {1}{2^{3}}}+{\frac {1}{2^{4}}}

The geometric series of a repeating decimal can be represented in summation. For example:

\sum _{i=1}^{\infty }{\frac {3}{10^{i}}}=0.333333...={\frac {1}{3}}

The concept of an integral is a limit of sums, with the area under a curve being defined as:

\lim _{n\to \infty }\sum _{i=1}^{n}f(x_{i}^{*})\Delta x

Product (mathematics)

References

↑ "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-08-16.
↑ Weisstein, Eric W. "Sum". mathworld.wolfram.com. Retrieved 2020-08-16.
↑ ^3.0 ^3.1 ^3.2 "Calculus I - Summation Notation". tutorial.math.lamar.edu. Retrieved 2020-08-16.

Other websites

Media related to Summation at Wikimedia Commons
Sigma Notation Archived 2015-09-21 at the Wayback Machine on PlanetMath
Derivation of Polynomials to Express the Sum of Natural Numbers with Exponents Archived 2013-02-18 at the Wayback Machine

Read other articles:

Kapar (sampah kayu)

Artikel ini sebatang kara, artinya tidak ada artikel lain yang memiliki pranala balik ke halaman ini.Bantulah menambah pranala ke artikel ini dari artikel yang berhubungan atau coba peralatan pencari pranala.Tag ini diberikan pada Oktober 2022. Timbunan kapar yang terbawa arus ke tepi pantai. Kapar[1] atau aisibia[2] adalah kayu-kayu buangan yang hanyut di sungai atau laut,[3] atau terdampar di kawasan pesisir. Kapar adalah salah satu jenis dari sampah laut yang dapat ...

1893 in paleontology

Overview of the events of 1893 in paleontology List of years in paleontology (table) … 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 … In science 1890 1891 1892 1893 1894 1895 1896 Art Archaeology Architecture Literature Music Philosophy Science +... Paleontology or palaeontology is the study of prehistoric life forms on Earth through the examination of plant and animal fossils.[1] This includes the study of body fossils, ...

Casuarina Islets

Islands in South Australia This article is about the pair of islets in South Australia. For other uses, see Casuarina (disambiguation). Casuarina IsletsCape Du Couedic and the two Casuarina Islands, circa 1912 (State Library of South Australia,SRG-67-20-21)Casuarina IsletsGeographyLocationGreat Australian BightCoordinates36°04′01″S 136°42′08″E / 36.06694°S 136.70222°E / -36.06694; 136.70222Area4 ha (9.9 acres)[1]AdministrationAustralia The Casu...

Bahasa Sindh

Bahasa Sindhi سنڌي सिन्धी ਸਿੰਧੀ Dituturkan diSindh, Pakistan dan Gujarat, India. Juga di berbagai penjuru dunia seperti Hong Kong, Oman, Filipina, Indonesia, Singapura, Uni Emirat Arab, Inggris, Amerika Serikat, Kanada, Australia, Tiongkok, Prancis, Jepang, Malaysia, Arab Saudi, QatarWilayahSeluruh duniaPenutur75 juta Rincian data penutur Jumlah penutur beserta (jika ada) metode pengambilan, jenis, tanggal, dan tempat.[1] 24.600.000 (2019, Bahasa ibu)21....

Aborigines Protection Act 1909

New South Wales legislation, repealed Aborigines Protection Act 1909Parliament of New South Wales Long title An Act to provide for the protection and care of aborigines; to repeal the Supply of Liquors to Aborigines Prevention Act; to amend the Vagrancy Act, 1902, and the Police Offences (Amendment) Act, 1908; and for purposes consequent thereon or incidental thereto. CitationAct No. 25, 1909Royal assent20 December 1909RepealsSupply of Liquors to Aborigines Prevention Act 1867Repealed byAbori...

Синелобый амазон

Синелобый амазон Научная классификация Домен:ЭукариотыЦарство:ЖивотныеПодцарство:ЭуметазоиБез ранга:Двусторонне-симметричныеБез ранга:ВторичноротыеТип:ХордовыеПодтип:ПозвоночныеИнфратип:ЧелюстноротыеНадкласс:ЧетвероногиеКлада:АмниотыКлада:ЗавропсидыКласс:Пт�...

Pays-Bas au Concours Eurovision de la chanson 1973

Pays-Basau Concours Eurovision 1973 Données clés Pays Pays-Bas Chanson De oude muzikant Interprète Ben Cramer Langue Néerlandais Sélection nationale Radiodiffuseur NOS Type de sélection Finale nationaleÉmission télévisée : Nationaal Songfestival 1973Sélection interne (artiste) Date 28 février 1973 Lieu Amsterdam Concours Eurovision de la chanson 1973 Position en finale 14e (69 points) 1972 1974 modifier Les Pays-Bas ont participé au Concours Eurovision de la chanson 1...

Bartosz Salamon

Bartosz Salamon Bartosz Salamon nel 2017 Nazionalità Polonia Altezza 196[1] cm Peso 89[1] kg Calcio Ruolo Difensore Squadra Lech Poznań Carriera Giovanili 1999-2004 Concord2004-2007 Lech Poznań2007-2010 Brescia Squadre di club1 2008-2010 Brescia16 (0)2010-2011→ Foggia27 (2)2011-2013 Brescia46 (4)2013 Milan0 (0)2013-2014 Sampdoria2 (0)2014-2015→ Pescara31 (1)[2]2015-2017 Cagliari48 (2)2017-2018 SPAL...

约翰斯顿环礁

此條目可参照英語維基百科相應條目来扩充。 (2021年5月6日)若您熟悉来源语言和主题，请协助参考外语维基百科扩充条目。请勿直接提交机械翻译，也不要翻译不可靠、低品质内容。依版权协议，译文需在编辑摘要注明来源，或于讨论页顶部标记{{Translated page}}标签。约翰斯顿环礁Kalama Atoll 美國本土外小島嶼 Johnston Atoll 旗幟颂歌：《星條旗》The Star-Spangled Banner約翰斯頓環礁�...

Park Row, Leeds

Park Row Park Row is a street in Leeds city centre, West Yorkshire, England. It divides the main financial districts from the main retail districts and forms a spine between City Square and The Headrow, two of Leeds' most sought-after addresses. The street forms the western flank of the Public Transport Box, and as such is mostly reserved for buses, taxis and cyclists, especially since reconfiguration 202-2021 as part of city-centre-wide traffic infrastructure changes.[1] Between the...

George Loewenstein

American educator and economist George LoewensteinGeorge LoewensteinBorn (1955-08-09) August 9, 1955 (age 68)NationalityAmericanAcademic careerInstitutionCarnegie Mellon UniversityFieldBehavioral economicsNeuroeconomicsAlma materYale University (Ph.D. 1985)Brandeis University (B.A. 1977)InfluencesRichard ThalerContributionsIntertemporal choiceInformation at IDEAS / RePEc George Loewenstein (born August 9, 1955)[1] is an American educator and economist. He is the He...

DTMB

Halaman ini berisi artikel tentang standar televisi digital Tiongkok. Untuk bandara dengan kode ICAO DTMB, lihat Bandar Udara Internasional Habib Bourguiba. Artikel ini bukan mengenai DVB atau URI. Daftar standar penyiaran televisi digital Standar DVB (negara) DVB-T (terestrial) DVB-T2 DVB-S (satelit) DVB-S2 DVB-C (kabel) DVB-C2 DVB-H (handheld) DVB-SH (satelit) Standar ATSC (negara) ATSC (terestrial/kabel) ATSC 2.0 ATSC-M/H (mobile/handheld) Standar ISDB (negara) ISDB-T (terestrial) ISDB-T I...

Мужская сборная Дании по кабадди

Мужская сборная Дании по кабадди Международная федерация Международная федерация кабадди (англ. International Kabaddi Frderation)[1], Всемирная федерация кабадди (англ. World Kabaddi Federation)[2] Национальная федерация Федерация кабадди Дании (англ. Kabaddi Federation of Denmark)[3] Мужска�...

Dutch Baroque architecture

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Dutch Baroque architecture – news · newspapers · books · scholar · JSTOR (April 2011) (Learn how and when to remove this message) Royal Palace (Amsterdam): Jacob van Campen, 1646. Oostkerk, Middelburg: Arent van 's-Gravesande [nl], 1667. Dutch Baro...

Henderson County, Kentucky

County in Kentucky, United States Not to be confused with Henderson, Kentucky. County in KentuckyHenderson CountyCountyHenderson County courthouse in Henderson, KentuckyLocation within the U.S. state of KentuckyKentucky's location within the U.S.Coordinates: 37°48′N 87°34′W / 37.8°N 87.57°W / 37.8; -87.57Country United StatesState KentuckyFounded1798Named forRichard HendersonSeatHendersonLargest cityHendersonArea • Total466 sq mi...

Netball at the 1998 Commonwealth Games

Netball at the 1998 Commonwealth GamesVenueKuala LumpurDates14 – 21 September 1998Nations12Medalists Australia New Zealand EnglandManchester 2002 → The netball competition at the 1998 Commonwealth Games took place in Kuala Lumpur, Malaysia from 14 – 21 September 1998.[1] Australia won the gold medal.[2] Results Group stages Group A Team 1 Team 2 Score Australia Malaysia 85-17 England Barbados 51-29 Jamaica Canada 74-36 Aus...

هام ليك

هام ليك الإحداثيات 45°15′16″N 93°12′57″W / 45.254444444444°N 93.215833333333°W / 45.254444444444; -93.215833333333 [1] تقسيم إداري البلد الولايات المتحدة[2] التقسيم الأعلى مقاطعة أنوكا خصائص جغرافية المساحة 92.883131 كيلومتر مربع92.504526 كيلومتر مربع (1 أبريل 2010) ارتفا...

Oscar's Oasis

Oscar's OasisKartu judul Oscar's OasisSutradaraDavid GarciaTae-Sik ShinNegara asalPrancisKorea SelatanBahasa asliBisuJmlh. musim1Jmlh. episode78 + 1 Oasis + 7 Ooohhh AsisProduksiProduser eksekutifGenevieve DexterSung-Jai AhnCorinne KouperEugene KangTom van WaverenGuillaume HellouinDurasi7.5 menitDistributorCake EntertainmentRilis asliJaringanCanal+ Family (versi asli)Disney Channel Asia(versi asli)Disney Channel AustraliaPOP (UK)Nintendo 3DS(Nintendo Video [Pop])Cartoon Network Latin America...

Brønderslev

City in North Jutland Region, DenmarkBrønderslevCity Coat of armsBrønderslevLocation in DenmarkShow map of DenmarkBrønderslevBrønderslev (North Jutland Region)Show map of North Jutland RegionCoordinates: 57°16′10″N 9°56′50″E / 57.26944°N 9.94722°E / 57.26944; 9.94722CountryDenmarkRegionNorth Jutland RegionMunicipalityBrønderslev MunicipalityArea • Urban8.12 km2 (3.14 sq mi)Population (2024) • Urban12,842...

Judo ai XVIII Giochi del Mediterraneo

Voce principale: XVIII Giochi del Mediterraneo. I tornei di judo ai XVIII Giochi del Mediterraneo si sono svolti dal 27 al 29 giugno 2018 al Pabellón de Cambrils. Si è gareggiato in 14 diverse categorie di peso, di cui sette maschili e sette femminili. Indice 1 Calendario 2 Risultati 2.1 Uomini 2.2 Donne 3 Medagliere 4 Collegamenti esterni Calendario Il calendario delle gare è stato il seguente: ● Finali Giugno/Luglio 22 23 24 25 26 27 28 29 30 1º 5 &...

PROFILPELAJAR.COM

Sum

Sigma notation

Properties

Applications

Related pages

References

Further reading

Other websites

Read other articles:

Kapar (sampah kayu)

1893 in paleontology

Casuarina Islets

Bahasa Sindh

Aborigines Protection Act 1909

Синелобый амазон

Pays-Bas au Concours Eurovision de la chanson 1973

Bartosz Salamon

约翰斯顿环礁

Park Row, Leeds

George Loewenstein

DTMB

Мужская сборная Дании по кабадди

Dutch Baroque architecture

Henderson County, Kentucky

Netball at the 1998 Commonwealth Games

هام ليك

Oscar's Oasis

Brønderslev

Judo ai XVIII Giochi del Mediterraneo