Inchubekelembili arithmetical

Imisebenzi ye-inchubekelembili izibalo kwakukhona ezikhathini zasendulo. Bavele zabuzwa izixazululo, ngoba waba isidingo esisebenzayo.

Ngokwesibonelo, kwelinye papyrus yaseGibhithe lasendulo, kokuba okuqukethwe zezibalo, - papyrus Rhind (XIX leminyaka BC) - iqukethe inkinga enjalo: ukwehlukana izinyathelo eziyishumi yokusanhlamvu abantu abayishumi, uma uma umehluko phakathi ngamunye kubo ingenye-yesishiyagalombili izinyathelo ".

Futhi emibhalweni zezibalo ngokunqoba kwamaGreki asendulo, kukhona theorems nenhle ehlobene inchubekelembili izibalo. Ngakho, Hypsicles Alexandria (II ekhulwini BC), imali eningi imisebenzi ezithakazelisayo futhi wanezela amabhuku nane kuya "ekuqaleni" kokuphila Euclid washayelwa umbono: "Esikhathini inchubekelembili izibalo nokuba ngisho inani lamalungu, inani lamalungu Engxenyeni yesibili ezingaphezu kuka isamba amalungu 1- lesibili multiple of esigcawini 1/2 lamalungu. "

Sithatha inani ngokungadingekile izinombolo yemvelo (ngaphezu kuka-zero), 1, 4, 7, ... n-1, n, ..., okuthiwa ukulandelana kwamanani.

Lisho ukulandelana i. izinombolo ngokulandelana abizwa ngokuthi amalungu ayo ngokuvamile ezikhonjiswe tinhlavu indices, okuyinto ukhombise nenombolo ye-serial ilungu (a1, A2, A3 ... ukufunda: «lokuqala», «a yesibili», «a-egeza 3" nokunye ).

Ukulandelana kungaba elingapheli noma elinganiselwe.

Futhi iyini inchubekelembili izibalo? Kuyaqondakala njengoba ukulandelana kweenomboro etholwe kwengezwa ilungu odlule (n) inani elifanayo d, okuyinto ukuqhubeka umehluko.

Uma d <0, khona-ke siba inchubekelembili ngincipha. Uma d> 0 ke Kuleli qoqo kubhekwa okwandisa.

inchubekelembili Aritmethikhi libizwa ezilinganiselwe, uma sicabanga ezimbalwa kwamalungu alo okuqala kuphela. Lapho eziningi kakhulu amalungu ke ine inchubekelembili elingapheli.

Noma yimuphi inchubekelembili izibalo enikezwa ifomula elandelayo:

i = kN + b, kuyilapho b futhi k - ezinye izinombolo.

isitatimende Kasibili kweqiniso, okuyinto reverse: uma ukulandelana enikezwa ifomula efanayo, ncamashi ke ukuqhubeka izibalo, okuyinto ine impahla:

1. Ilungu ngalinye inchubekelembili - arithmetic kusho ukuthini igama elithi odlule bese.
2. : Uma, kusukela wesibili, ilungu ngalinye - arithmetic kusho ukuthini igama elithi langaphambilini, futhi okwalandela, okungukuthi, uma isimo, lokhu ukulandelana - i inchubekelembili izibalo. Lokhu ukulingana kokubili uphawu kwenqubekela phambili, ngakho-ke, esivame ukubizwa ngokuthi isici sobuntu inchubekelembili.
   Ngokufanayo, theorem kuyiqiniso ukuthi libonise lokhu impahla: ukulandelana - i inchubekelembili izibalo kuphela uma lokhu kwesibalo kuyiqiniso ngenxa yanoma yisiphi kulezi amalungu ukulandelana, uthome yesibili.

A impahla isici noma iziphi izinombolo ukuze ukuqhubeka ezine izibalo zingase zesikholwa ekuseni + = ak + al, uma n + m = k + l (m, n, k - nenani inchubekelembili).

Esimeni inchubekelembili izibalo yanoma yimuphi (N-th) ilungu oyifunayo zingatholakala ngokusebenzisa le ndlela elandelayo:

i = a1 + d (n-1).

Ngokwesibonelo: ilungu lokuqala (a1) i inchubekelembili izibalo iyanikezwa futhi ilingana ezintathu, futhi umehluko (d) uyalingana ezine. Thola ezidingekayo amane nanhlanu ilungu Kuleli qoqo. a45 = 1 + 4 (45-1) = 177

Formula i = ak + d (n - k) ukunquma eside n-th i inchubekelembili izibalo ngokusebenzisa ngamunye ilungu layo-k-th enikeziwe uma aziwa.

Sum ngokulandela inchubekelembili izibalo (sicabangela amalungu n lokuqala inchubekelembili ezilinganiselwe) ibalwa kanje:

Sn = (a1 + i) n / 2.

Uma wazi umehluko izibalo ebangeni lelilandzelako, futhi ilungu lokuqala, ukubala nezinye ifomula ewusizo:

Sn = ((2a1 + d (n-1)) / 2) * n.

Ukudlondlobala isamba izibalo okuyindawo ehlanganisa amalungu n, zibalwa ngale ndlela elandelayo:

Sn = (a1 + i) * n / 2.

Ukukhethwa amafomula tekubala kuncike kule mibandela futhi izinkinga idatha kokuqala.

izinombolo Yemvelo iyiphi inombolo efana 1,2,3, ..., n, ...- Ngokwesibonelo elula i inchubekelembili izibalo.

Ngaphezu kwalokho kukhona inchubekelembili izibalo kanye weJiyomethri okuyinto possesses the izakhiwo kanye nezici.