Lissafi da kuma samun ci gaban da kaddarorin

Lissafi da kuma samun ci gaban yana da muhimmanci a ilmin lissafi kamar yadda wani kimiyya, da kuma amfani da muhimmancin, tun yana da wani musamman m ikon yinsa, ko da a cikin mafi girma da lissafi, ga misali, a cikin ka'idar jerin. A farko bayani a kan irin ci gaban da ya zo mana daga zamanin d Misira, musamman a cikin wani nau'i na sanannun matsalar da Rhind Papyrus bakwai tare da bakwai Cats. Bambance-bambance na wannan aiki da aka maimaita sau da yawa a daban-daban sau daga sauran al'ummai. Ko da Velikiy Leonardo Pizansky, da aka sani da Fibonacci (XIII c.), Ya yi magana da ita cikin "Littafi na Abacus."

Saboda haka cewa lissafi ci gaban yana da wani tsoho tarihi. Yana wakiltar wani lamba jerin tare da wani nonzero farko mamba, kuma kowace m, da suka fara da na biyu ne m da halitta baya komawa dabara a akai, nonzero lambar da ake kira hada ci gaban (da shi kullum kaddamarda amfani da harafin q).
Babu shakka, ana iya gano ta rarraba kowace m lokaci na da jerin to baya, Ina nufin z 2: z 1 = ... = zn: z n-1 = .... Saboda haka, domin mafi aiki ci gaban (zn) Yã isa ya san da darajar da farko lokaci na hada da y 1 q.

Alal misali, bari z 1 = 7, q = - 4 (q <0), sa'an nan da wadannan lissafi ci gaban da aka samu 7 - 28, 112 - 448, .... Kamar yadda ka gani, sakamakon jerin ne ba monotone.

Ka tuna cewa wani sabani jerin monotonous (kara / ragewa) a lokacin da daya daga cikin Membobinta bi mafi / kasa da baya daya. Alal misali, da jerin 2, 5, 9, ..., kuma -10, -100, -1000, ... - Monotone, na biyu daya - a ragewa lissafi ci gaban.

A cikin akwati inda q = 1, duk da mambobi ana same su zama, kuma shi ne ake kira da akai ci gaban.

A jerin shi ne ci gaban irin wannan, dole ne gamsar da wadannan dole da kuma isa yanayin, wato: ya fara daga na biyu, kowane daga cikin Membobinta yayi zama na lissafi nufin na makwabta members.

Wannan dukiyar damar karkashin wasu biyu m binciken sabani lokaci ci gaban.

n-th lokaci dabam dabam saukin samu da dabara: zn = z 1 * q ^ (n-1), z sanin farko memba 1 da kuma hada q.

Tun da yawan jerin yana da wani Naira Miliyan Xari, sa'an nan da 'yan sauki lissafin ba mu da wani dabara yin lissafi da Naira Miliyan Xari da farko ci gaban members, wato:

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

Maye gurbin, a cikin dabara ta magana darajar zn z 1 * q ^ (n-1) kafin su sami wani biyu Naira Miliyan Xari dabara na da ci gaban: S n = - Z1 * (q ^ n - 1) / (1 - q).

Ne ya cancanci da hankali da wadannan ban sha'awa, gaskiya ne: lãka kwamfutar hannu samu a tono na zamanin d Babila, wanda yana nufin VI. BC, ya ƙunshi ƙwarai hanyar da Naira Miliyan Xari 1 + 2 + ... + 22 + 29 daidaita 2 zuwa ta goma ikon debe 1. A bayani na wannan sabon abu ya ba tukuna aka samu.

Mun lura daya daga cikin kaddarorin da lissafi ci gaban - akai aiki da membobinta, spaced a daidai nisa daga bangon da jerin.

Na musamman muhimmancin daga kimiyya ra'ayi, irin wannan abu a matsayin iyaka lissafi ci gaban da kuma kirga ta adadin. Feminism lafazin faransanci (yn) - a lissafi ci gaban da ciwon hada q, gamsarwa da yanayin | q | <1, ta adadin za a kira su da iyaka zuwa ga abin da muka riga ya san Naira Miliyan Xari ta farko members, tare da Mai girma karuwa da n, to, suna da a da shi gabatowa rashin iyaka.

Nemo wannan adadin a sakamakon yin amfani da dabara:

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

Kuma, kamar yadda kwarewa ya nuna, domin bayyana sauki daga wannan ci gaban da aka boye wata babbar aikace-aikace m. Alal misali, idan muka yi wani jerin murabba'ai bisa ga wadannan algorithm, a haɗa da midpoints na gabanin, su yankin samar da wani iyaka lissafi ci gaban ciwon hada 1/2. A wannan ci gaban tsari da kuma yanki na triangles, samu a kowane mataki na yi, kuma ta ware Naira Miliyan Xari ne daidaita da yankin na asali square.