Mapangidwe, Sekondale ndi sukulu
Kupitilira zojambula. CHITSANZO chigamulo
Taganizirani mzere.
7 28 112 448 1792 ...
chikusonyeza bwino ndithu kuti mtengo wa aliyense wa zanyengo kuposa m'mbuyomu ndendende kanayi. Choncho, zino ndi kupitilira.
kupitilira geometrical otchedwa wopandamalire ndondomeko ya manambala, chinthu chachikulu ndicho chiwerengero zotsatirazi analandira kuchokera pamwamba ndi kuchulukitsa ndi ena nambala yawo. Zimenezi ndi zimenenso ndi chilinganizo zotsatirazi.
ndi z 1 = ndi z · Q , pamene z - chiwerengero cha zinthu anasankha.
Choncho, z ∈ N.
nthawi imene sukulu amaphunzira zojambula kupitilira - 9 kalasi. Zitsanzo kudzakuthandizani kudziwa zinthu zosiyana:
0,25 0.125 0.0625 ...
18 February 6 ...
Kuchokera pa chilinganizo ichi, kupitirira wa chimene chachititsa ndi akapezedwe motere:
Ngakhale Q, kapena b z sangakhale ziro. Komanso, aliyense wa miyambo ya mndandanda wa manambala kupitilira sayenera ziro.
Choncho, kuona nambala yotsatira zingapo, kuchulukitsa yotsirizira ndi Q.
Kuthandauza kupitilira, muyenela mwachindunji chinthu choyamba kwa iyo ndi chimene chachititsa. Pambuyo kuti n'zotheka kupeza aliyense wa mamembala awa ndi kuchuluka kwawo.
mitundu
Malinga Q ndi 1, kupitirira izi lagawidwa mitundu ingapo:
- Ngati 1, ndi Q ali wamkulu kuposa wina, ndiye zinayendera - kuwonjezeka ndi aliyense walowa motsatizana kupitilira zojambula. Zitsanzo zake ndi zofunikila pansipa.
Mwachitsanzo: 1 = 3, Q = 2 - wamkulu kuposa umodzi, magawo onse.
Ndiye ndondomeko ya manambala akhoza kulembedwa monga:
3 6 12 24 48 ...
- Ngati | Q | zosakwana munthu, mwachitsanzo, ndi lofanana chulutsa ndi magawano, ndi kupitirira ndi chofanana - kucheperachepera kupitilira zojambula. Zitsanzo zake ndi zofunikila pansipa.
Mwachitsanzo: 1 = 6, Q = 1/3 - 1 ndi wamkulu kuposa wina, Q - zochepa.
Ndiye ndondomeko ya manambala akhoza kulembedwa motere:
June 2 2/3 ... - zinthu mbali iliyonse kwambiri kuwatsatira ndi 3 zina.
- Alternating. Ngati Q <0, zizindikiro za chiwerengero cha akuyambira alternating zonse kaya 1, ndi zinthu za kuchuluka kapena kuchepa.
Mwachitsanzo: 1 = -3, Q = -2 - onse ali ochepera ziro.
Ndiye ndondomeko ya manambala akhoza kulembedwa monga:
3, 6, -12, 24, ...
chilinganizo
Ntchito yabwino, pali zambiri progressions zojambula za mitunduyi ndi:
- Chilinganizo z-TH yaitali. Timatha ndi mawerengedwe a amafotokozera mu chiwerengero zochepa popanda kuwerengetsa manambala m'mbuyomu.
Chitsanzo: Q = 3, ndi = 1 4. chofunika kuwerengera wachinayi mchitidwe kupitirira.
Anakonza: a = 4 4 3 · 4-1 · 3 = 4 3 = 4 · 27 = 108.
- Uwerenge zinthu woyamba, amene chiwerengero ndiyofanana ndi z. Timatha ndi mawerengedwe Uwerenge zinthu zonse mwa ndondomeko ya ku z palimodzi.
≠ 0, motero, Q si 1 - (Q 1) Popeza (1- Q) zili chimene chachititsa, ndiye.
Dziwani: ngati Q = 1, ndiye kupitirira kuti anaimira angapo umasinthasintha kubwereza chiwerengero.
Kuchuluka exponentially Zitsanzo: 1 = 2, Q = -2. Kuwerengetsa S 5.
Yankho: S 5 = 22 - mawerengedwe chilinganizo.
- Kuchuluka ngati | Q | <1 ndi pamene z amamuchititsa osawerengeka.
Mwachitsanzo: 1 = 2, Q = 0.5. Pezani pamodzi.
Yankho: S z = 2 × = 4
Ngati ife kuwerengera ndalama za anthu angapo a bukhuli, mudzaona kuti Ndithudi udaperekedwa anayi.
S z = + 1 + 2 0.5 + 0,25 + 0,125 + 0.0625 = 3.9375 4
Ena katundu:
- A katundu khalidwe. Ngati matenda otsatirawa Zikupereka kwa z aliyense, patsidwa mndandanda n'zosangalatsa kumva - ndi kupitirira zojambula:
ndi z 2 = A z -1 · A z + 1
- Ndi m'bwalo la chiwerengero ndi exponentially mwa Kuwonjezera wa mabwalo a manambala ena awiri mu mzere iliyonse, ngati iwo ali equidistant ku mchitidwe wa.
2 z = ndi z - T 2 + ndi z + T 2 komwe T - mtunda pakati pa manambala awa.
- zinthu kumasiyana ndi nthawi Q.
- The logarithms mbali ya patsogolo komanso kupanga kupitilira, koma masamu, ndiye aliyense wa iwo kuposa wina wapitawu nambala inayake.
Zitsanzo za zina mavuto chakale
Kumvetsetsa zimene kupitilira zojambula, ndi zitsanzo kusankha kwa kalasi 9 angakuthandizeni.
- Terms ndi zinthu: 1 = 3, 3 = 48. kupeza Q.
Yankho: lililonse mchitidwe motsatizana zambiri kuposa Q yapita nthawi. M'pofunika kufotokoza ena zinthu mwa zina kudzera chimene chachititsa.
Choncho, 3 = Q 2 · 1
Pamene m'malo Q = 4
- Zokwaniritsa: 2 = 6, ndi = 3 12. kuwerengetsa S 6.
Yankho: Kuti tichite zimenezi, suffices kupeza Q, chinthu choyamba ndipo mmalo mwa njira.
3 = Q · 2, chotero, Q = 2
2 = Q · A 1, kotero ndi = 1 3
S = 6 189
- · A 1 = 10, Q = -2. Pezani chinthu chachinayi cha kupitirira.
Yankho; chakwanira kufotokoza zinthu chachinayi loyamba ndi kudzera chimene chachititsa lapansi.
4 3 = Q · a = 1 -80
Ntchito Mwachitsanzo:
- Bank kasitomala zathandizira Uwerenge rubles 10,000 umene chaka kasitomala ndi kuchuluka yaikulu zidzawonjezedwa 6% ya izo. Kodi ndalama ndi nkhani patatha zaka 4?
Yankho: The koyamba kuchuluka wofanana rubles 10 chikwi. Choncho, chaka pambuyo ndalama ku nkhani adzakhala kuchuluka wofanana 10000 + 10000 = 10000 · 0,06 · 1,06
Choncho, kuchuluka m'nkhaniyi ngakhale chaka chimodzi adzalamulira motere:
(10000 · 1.06) · 10000 · 0,06 + 1,06 = 1,06 · 1.06 · 10000
Ndiko kuti, chaka kuchuluka kuchuluka kwa nthawi 1,06. Choncho, kupeza chiwerengero cha nkhani patatha zaka 4, suffices kupeza chachinayi mchitidwe kupitilira, lopatsidwa chinthu choyamba wofanana 10 chikwi, ndi chimene chachititsa wofanana 1,06.
S = 1,06 · 1,06 · 1,06 · 1,06 · 10000 = 12625
Zitsanzo za mavuto masovedwe Muwerenge:
Mu mavuto osiyanasiyana ntchito kupitirira zojambula. Chitsanzo chopeza ndalama zikhoza kukhazikitsidwa motere:
1 = 4, Q = 2, kuwerengera S 5.
Yankho: deta zonse zofunikira mawerengedwe amadziwika, chabe mmalo iwo mu njira.
S 5 = 124
- 2 = 6, ndi = 3 18. kuwerengera ndalama za choyamba zinthu zisanu ndi chimodzi.
yankho;
The Geom. patsogolo chilichonse mchitidwe ikuluikulu yotsatirayi kuposa m'mbuyomu nthawi Q, kutanthauza kuti kuwerengera ndalama muyenera kudziwa zinthu 1 ndi chimene chachititsa Q.
2 · Q = 3
Q = 3
Mofananamo, kufunika kupeza 1, 2 ndi kuzindikira Q.
1 · Q = 2
1 = 2
Ndiyeno suffices m'malo deta wodziwika mu kuchuluka chilinganizo.
S 6 = 728.
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