Arithmetical ci gaban

Ayyuka na wani ilmin lissafi ci gaban wanzu a zamanin da. Sun bayyana da nema mafita, domin suna da wani m larura.

Alal misali, a daya daga cikin papyri na zamanin d Misira, da ciwon ilmin lissafi abun ciki, - Papyrus Rhind (XIX karni BC) - ƙunshi irin wannan matsala: raba goma matakan na hatsi ga goma mutane, bayar idan bambanci tsakanin kowanne daga cikinsu shi ne daya-takwas daga cikin matakan. "

Kuma a cikin ilmin lissafi rubuce-rubucen na zamanin d Girkawa, akwai m theorems alaka da wani ilmin lissafi ci gaban. Saboda haka, Hypsicles Alexandria (II karni BC), maki mai yawa ban sha'awa ayyuka, da kuma kara goma sha hudu da littattafai da "farkon" na Euclid tsara da ra'ayin: "A cikin ilmin lissafi ci gaban da ciwon da wani ko da yawan mambobi, da adadin mambobi na biyu da rabi fiye da Naira Miliyan Xari da membobin 1- na biyu zuwa mahara na da square 1/2 na mambobin. "

Mu dauki wani sabani yawan halitta lambobi (mafi girma daga sifili), 1, 4, 7, ... n-1, n, ..., wanda aka kira na lamba jerin.

Suturta da jerin wani. jerin lambobi suna kira membobinta da kuma yawanci denoted haruffa da fihirisa, wanda ya nuna da serial number na memba (A1, A2, A3 ... karanta: «wani farko», «na biyu», «wata 3-wanka", kuma haka a kan ).

A jerin iya zama iyaka ko guntun.

Kuma abin da yake ilmin lissafi ci gaban? An fahimci matsayin wani jeren lambobi samu ta ƙara baya memba (n) tare da wannan yawan d, wanda shi ne bambanci ci gaban.

Idan d <0, to, muna da wani ragewa ci gaban. Idan d> 0, to, wannan ci gaban da aka dauke su a kara.

Ilmin lissafi ci gaban da aka kira guntun, idan muka yi la'akari ne kawai da 'yan ta farko members. Lokacin da manya-manyan yawan mambobin yana da wani iyaka ci gaban.

Duk wani ilmin lissafi ci gaban da aka ba da da wadannan dabara:

an = kn + b, yayin da b da kuma k - wasu lambobi.

Babu shakka gaskiya sanarwa, wanda shi ne baya: idan da jerin aka bai da wani irin dabara, shi ne daidai ilmin lissafi ci gaban, wanda yana da kaddarorin:

1. Kowane memba na ci gaban - da ilmin lissafi nufin na baya ambatacce sa'an nan.
2. : Idan, fara daga na biyu, kowane memba - da ilmin lissafi nufin na baya ambatacce, kuma m, watau, idan da yanayin, wannan jerin - wani ilmin lissafi ci gaban. Wannan daidaito ne duka da wata ãyã ci gaba, saboda haka, fiye kira a matsayin wata halayyar alama na ci gaban.
   Hakazalika, Theorem gaskiya ne cewa nuna wannan dukiya: da jerin - wani ilmin lissafi ci gaban kawai idan wannan lissafi shi ne gaskiya ga wani daga cikin membobin da jerin, suka fara da na biyu.

A halayyar dũkiyar wani lambobi ga hudu ilmin lissafi ci gaban iya bayyana ta da wani + am = AK + al, idan n + m = k + l (m, n, k - yawan ci gaban).

A wani ilmin lissafi ci gaban da wani so (N-th) memba za a iya samu ta hanyar yin amfani da wadannan dabara:

an = A1 + d (n-1).

Ga misali: na farko memba (A1) a cikin wani ilmin lissafi ci gaban da aka ba da kuma daidai da uku, da kuma bambanci da (d) ne daidai da hudu. Nemo dole zuwa arba'in da biyar memba na wannan ci gaban. a45 = 1 + 4 (45-1) = 177

Formula wani = AK + d (n - k) domin sanin n-th lokaci na wani ilmin lissafi ci gaban ta hanyar kowane daga cikin k-th memba bayar idan ka sani.

Sum sharuddan wani ilmin lissafi ci gaban (dauka na farko n mambobi guntun ci gaban) da aka lasafta kamar haka:

SN = (A1 + wani) n / 2.

Idan ka san bambanci a ilmin lissafi ci gaban, na farko kuma memba, yin lissafi da sauran amfani dabara:

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

An ware Naira Miliyan ilmin lissafi ci gaban da qunshi n members, an lasafta kamar haka:

SN = (A1 + wani) * n / 2.

Selection dabarbari ga lissafin ya dogara da yanayi da kuma matsalolin na farko data.

Halitta lambobin wani adadin kamar 1,2,3, ..., n, ...- sauki misali na wani ilmin lissafi ci gaban.

Bugu da kari akwai wani ilmin lissafi ci gaban da na lissafi da ya mallaka da kaddarorin da kuma halaye.