Kutevedzana uye Nhevedzano: Tsanangudzo, Mhando, uye Mashandisirwo
Marongerwo nenhevedzano ipfungwa huru mumasvomhu dzine mashandisirwo akapararira muminda yakasiyana-siyana, kubva kumari kusvika kusainzi yemakombiyuta. Kunyange zvazvo pfungwa idzi mbiri dzakabatana, dzine hunhu hwakasiyana uye mashandisirwo akasiyana. Chinyorwa chino chichanyatsoongorora marongerwo nenhevedzano, kusanganisira tsananguro dzadzo, mhando, uye mashandisirwo adzo muhupenyu hwezuva nezuva.
Tsanangudzo yeKutevedzana
Muchidimbu, kutevedzana kwenhamba kunoenderana nemitemo yakati. Kutevedzana kwenhamba kunowanzo ratidzwa nechinyorwa \(a_n\), apo \(n\) iri nhamba yakakwana inoratidza nzvimbo yechinhu mukuteverana, uye \(a_n\) iri chinhu \(n\)th.
Muenzaniso wenhevedzano
Kana tine nhamba yemasvomhu inotangira pa2 ine musiyano wakafanana we3, saka zvinhu zvayo zvinotevera:
– \(a_1 = 2\)
– \(a_2 = 5\)
– \(a_3 = 8\)
- nezvimwewo.
Zvinhu izvi zvinotevera mutemo \(a_n = a_1 + (n-1)d\), apo \(a_1\) chiri chinhu chekutanga, uye \(d\) ndicho musiyano uripo pakati pezvinhu.
Tsanangudzo yeNhevedzano
Nhevedzano ihuwandu hwezvinhu zviri munhevedzano. Kana tiine nhevedzano \(a_1, a_2, a_3, \ldots, a_n\), saka nhevedzano inoumbwa ndi \(a_1 + a_2 + a_3 + \ldots + a_n\).
Muenzaniso weNhevedzano
Kana tine kutevedzana kwakafanana nemuenzaniso wapfuura:
– \(a_1 = 2\)
– \(a_2 = 5\)
– \(a_3 = 8\)
Saka nhevedzano inoumbwa kubva pachinhu chekutanga kusvika pachinhu chechitatu ndeye \(2 + 5 + 8 = 15\).
Mhando dzeSequences neSeries
Kutevedzana kweMasvomhu
Kutevedzana kwemasvomhu inzira yekuverenga nhamba umo musiyano uripo pakati pezvinhu zvinotevedzana usingachinji. Kana chinhu chekutanga chiri \(a_1\) uye musiyano usingachinji uri \(d\), saka chinhu \(n\)th chinogona kuwanikwa uchishandisa fomura:
\[ a_n = a_1 + (n-1)d \]
Muenzaniso:
Nhevedzano 2, 5, 8, 11, … inhevedzano yemasvomhu ine \(a_1 = 2\) uye \(d = 3\).
Mutsetse wearithmetic ihuwandu hwezvinhu zviri mumutsara wearithmetic. Huwandu hwezvinhu zvekutanga \(n\) zvemutsara wearithmetic hunowanikwa uchishandisa fomura:
\[ S_n = \frac{n}{2} \kuruboshwe( 2a_1 + (n-1)d \kurudyi) \]
Nhevedzano yeJomethri
Kutevedzana kwejometri inzira yekuverenga nhamba umo chiyero pakati penhengo dzinotevedzana chiri chisingachinji. Kana chinhu chekutanga chiri \(a_1\) uye chiyero chisingachinji chiri \(r\), saka chinhu \(n\)th chinogona kuwanikwa uchishandisa fomura:
\[ a_n = a_1 \cdot r^{(n-1)} \]
Muenzaniso:
Kutevedzana kwenhamba 3, 6, 12, 24, … kutevedzana kwenhamba dzemajiometri nenhamba \(a_1 = 3\) uye \(r = 2\).
Nhevedzano yejometri ihuwandu hwezvinhu zviri munhevedzano yejometri. Huwandu hwezvinhu zvekutanga \(n\) zvenhevedzano yejometri hunowanikwa uchishandisa fomura:
\[ S_n = a_1 \frac{1-r^n}{1-r} \]
Mashandisirwo eSequences neSeries
Mari nehupfumi
Mumari, ma "sequences" ne "series" zvinowanzo shandiswa kuverenga kukosha kwemari yekudyara mune ramangwana. Semuenzaniso, muripo wepagore wakagadzika unogona kuenzaniswa se "mathractice sequence", nepo mubereko wakabatana uchigona kuenzaniswa se "geometric sequence".
Semuenzaniso, kana uine mari inodyarwa inokura gore rega rega nemari yakatarwa, ngatitii Rp 1.000.000 pagore, izvi zvinogona kuenzaniswa senzira yekuverenga. Kusiyana neizvi, kana mari inodyarwa ikawedzera pamutengo wechikwereti wakatarwa, ngatitii 5% pagore, saka izvi zvinogona kuenzaniswa senzira ye geometric.
Kuwedzera Kwevagari
Kukura kwevanhu kunogona kuverengerwa pachishandiswa nzira yejometri. Kana vanhu vakawanda vachikura pamwero usingachinji, ngatitii 2% pagore, saka gore rega rega vanhu vachave ne1.02 yakapetwa kupfuura huwandu hwevanhu vegore rapfuura, zvichigadzira nzira yejometri.
Sainzi yeKombuta
Musainzi yemakombiyuta, ma sequences ne series zvinoshandiswa muma algorithms nema data structures. Muenzaniso wakajairika kushandiswa kwema sequences mu dynamic programming, uko mhedzisiro ye n-th subproblem inochengetwa kugadzirisa dambudziko guru. Uyezve, Fibonacci sequence, ine zvinhu zviri muunganidzwa wezvinhu zviviri zvekare, inowanzoshandiswa muma algorithms akawanda anosanganisira kutsvaga kwakanaka uye kurongedza.
Zviratidzo uye Masisitimu
Munyaya dzezviratidzo nemasisitimu, Fourier series chishandiso chakakosha. Fourier series inotibvumira kuratidza zviratidzo zvenguva nenguva se sinusoidal sums. Izvi zvakakosha pakuongorora nekugadzira zviratidzo muinjiniya yemagetsi nekutaurirana.
Mhedziso
Kutevedzana kwezvikamu nezvikamu ipfungwa dzemasvomhu dzakakosha asi dzine simba, dzine mashandisirwo akapararira munzvimbo dzakasiyana-siyana. Kunzwisisa kutevedzana kwezvikamu nezvikamu kwakakosha kwete chete kumasvomhu chaiwo asiwo pakushandisa kwakakosha muhupenyu hwezuva nezuva. Kutevedzana kwezvikamu kunotibatsira kunzwisisa kurongeka uye mapatani, nepo kutevedzana kwezvikamu kuchitibatsira kunzwisisa huwandu hwezvinhu izvozvo.
Kuburikidza nechinyorwa chino, tinotarisira kuti vaverengi vachanzwisisa zviri nani pfungwa huru dzezvikamu nezvikamu, mhando dzakajairika, dzakadai semasvomhu nejometri, uye mamwe mashandisirwo anowanikwa muzvikamu zvakasiyana-siyana. Nekunzwisisa kwakasimba kwepfungwa idzi, tichave takagadzirira zviri nani kugadzirisa matambudziko akaomarara anogona kugadziriswa tichishandisa nzira dzakanaka dzemasvomhu.
