Inchubekelembili-Jomethri futhi izakhiwo zalo

inchubekelembili-Jomethri kubalulekile izibalo njengoba isayensi isicelo ukubaluleka, ngoba ine ububanzi ezibanzi kakhulu, ngisho e- mathematics ephakeme, isibonelo, imfundiso yokuziphendukela chungechunge. Ulwazi lokuqala ngenqubekela beza kithi kusukela eGibhithe lasendulo, ikakhulukazi ngesimo inkinga owaziwa we Rhind-papyrus, abantu abangamakhulu ayisikhombisa nge namakati eziyisikhombisa. Ukuhluka kwalo msebenzi yaphindwa izikhathi eziningi ngezikhathi ezahlukahlukene kwezinye izizwe. Ngisho Velikiy Leonardo Pizansky, eyaziwa ngokuthi Fibonacci (XIII c.), Wakhuluma naye yakhe "egwalweni Abacus."

Ngakho ukuthi ukuqhubeka weJiyomethri has enomlando wasendulo. It kujamele ukulandelana zezinombolo nelungu nonzero lokuqala, futhi ngamunye okwalandela, uthome yesibili kunqunywa siphindaphindeka owedlule Ukuphinda ifomula ngesikhathi, inombolo njalo nonzero owawubizwa zihilela inchubekelembili (ngokuvamile esiqokiwe usebenzisa q incwadi).
Ngokusobala, lingatholakala sokuhlukanisa ngamunye eside okwalandela wokulandelana zangaphambilini, isb z 2: z 1 = ... = Zn: z n-1 = .... Ngenxa yalokho, iningi umsebenzi inchubekelembili (Zn) eyanele ukuthi uyazi ukubaluleka ethemini lokuqala zifana futhi y 1 q.

Ngokwesibonelo, ake z 1 = 7, q = - 4 (q <0), khona-ke ukuqhubeka elandelayo weJiyomethri etholwe 7 - 28, 112 - 448, .... Njengoba ubona, ukulandelana okuholela akuyona ngephimbo elifanayo.

Khumbula ukuthi i-ukulandelana ngokungadingekile okuyisidina (okwandisa / nokuncipha) lapho omunye wamalungu ayo ulandele okuningi / okuncane kwalowo odlule. Ngokwesibonelo, ukulandelana 2, 5, 9, ..., futhi -10, -100, -1000, ... - Monotone, Neyesibili - a ngincipha inchubekelembili weJiyomethri.

Esimweni lapho q = 1, wonke amalungu kutholakala ukuthi, futhi iyaqhubeka ibizwa ngokuthi ukuqhubeka njalo.

Ukulandelana kwaba phambili yalolu hlobo, kumele ukwanelisa isimo elandelayo ezidingekayo futhi ezanele, okuyilezi: kusukela wesibili, ngamunye namalungu ayo kufanele abe asho weJiyomethri amalungu angomakhelwane.

Le mpahla ivumela ngaphansi ezithile okwatholakala emibili elandelanayo eside ngokungenasizathu inchubekelembili.

n-th eside exponentially atholakala kalula ifomula: Zn = z 1 * q ^ (n-1), z wazi ilungu lokuqala 1 kanye q zifana.

Kusukela ukulandelana kweenomboro has a isamba, ke izibalo ezimbalwa ezilula ukusinika ifomula ukubala isamba inchubekelembili lokuqala amalungu, okuyilezi:

S n = - (Zn * q - z 1) / (1 - q).

Njengoba ezothatha isikhundla, ku-formula yayo Inkulumo ukubaluleka Zn z 1 * q ^ (n-1) ukuthola isamba ifomula yesibili ukuqhubeka: S n = - Z1 * (q ^ n - 1) / (1 - q).

Ingabe azinake yokuthi elandelayo ezithakazelisayo: the isitini atholakala lapho kumbiwa wamandulo iBhabhiloni, okubhekisele VI. BC, iqukethe ngendlela ephawulekayo yinani lika-1 + 2 + ... + 22 + 29 ilingana 2 ukuya kweleshumi amandla lokususa 1. Incazelo zalesi simo ingakamiswa ezitholakele.

Siphawula omunye izakhiwo inchubekelembili weJiyomethri - umsebenzi njalo amalungu ayo, esilinganayo at amabanga alinganayo emikhawulweni ukulandelana.

Okubaluleke kakhulu kusukela iphuzu zesayensi of umbono, into efana inchubekelembili weJiyomethri okungenamingcele ekubaleni senani. Uzitshela ukuthi (yn) - umkhuba oqhubekayo wokubuka weJiyomethri kokuba zihilela q, wanelise isimo | q | <1, senani izobizwa umkhawulo maqondana okuyinto vele sesiyazi isamba kwamalungu alo okuqala, ngokwanda engenamingcele n ke ibe okungenani-ke esondela infinity.

Thola leli nani ngenxa kusetshenziswa indlela:

S n = y 1 / (1- q).

Futhi, njengoba okuhlangenwe nakho kuye kwabonisa, ngokuba lula okusobala Kuleli qoqo kufihliwe isicelo omkhulu ezingaba khona. Ngokwesibonelo, uma sakha ekulandelaneni izikwele ngokuvumelana algorithm ezilandelayo, ohlanganisa kwe-Midpoints of dlule fike ke akha square elingapheli inchubekelembili weJiyomethri kokuba zihilela 1/2. efanayo Ifomu ebangeni lelilandzelako nekunika endaweni onxantathu, etholwe esigabeni ngasinye ukwakhiwa, futhi isamba yayo ilingana endaweni isikwele yasekuqaleni.