Ho okumu, Secondary ka hoʻonaʻauao a me nā kula
Geometric Holomua. Laʻana i ka olelo hooholo
E noonoo oe i ka lalani.
7 28 112 448 1792 ...
Muli o kona kulana maopopo hōʻike i ka waiwai o kekahi o kona hehee wale oi ma mua o ka mea mua e like eha manawa. No laila, i kēia moʻo mea he Holomua.
geometrical Holomua kapaia mana loa kaʻina o nā helu, ka nui hiʻona o ka i mea i ua loaa mai ka mea ma luna o ke kēia helu ma ka hoonui ana kekahi definite helu. Keia ua kāheaʻia ma ka kēia haʻilula.
he Z +1 = ka Z · Q , kahi Z - helu o ka i koho hehee ai.
Alaila, Z ∈ N.
A manawa i ka wa a ke kula e? Anoee geometric Holomua - 9th papa. Ano he kumu hoʻohālike, e kōkua maopopo i ka manaʻo:
0,25 0,125 0,0625 ...
18 February 6 ...
Ma muli o kēia haʻilula, hiki ke loaʻa ka Holomua o ka denominator like penei:
Aole Q, a e Z hiki ole e 'Aʻohe. Kekahi, kela mea keia mea o na kumu o ka moʻo o ka helu Holomua e ole e 'Aʻohe.
Alaila, e ike i ka kekahi helu o ka helu, e hoonui i ka hope ma Q.
E hoakaka i kēia Holomua, e pono ke koho 'ia i ka hehee ai mua o ka mea a me ka denominator. Ma hope iho o ia mea, he mea hiki, e imi i kekahi o na kēia mau lala, a me ko lakou dala.
? ueo
Ke kaumaha ma muli o ka Q a me ka 1, keia Holomua ua maheleia i loko o kekahi mau ano:
- Inā he 1, a me ka Q mea oi o kekahi, alaila, he kaʻina - ka hana ana me kela a me keia ka mea i hahai ana ka mea mamuli o kekahi hehee ai o ka geometric Holomua. Ano he kumu hoʻohālike o ia mea, ua piha ma lalo nei.
Laʻana: he 1 = 3, Q = 2 - oi aku ma mua o ka lōkāhi, nā mea kiko'î.
A laila, he kaʻina o nā huahelu hiki ke palapalaia e like me:
3 6 12 24 48 ...
- Inā | Q | emi mai o kekahi, 'o ia hoʻi, ka mea, ua like ke multiplication ma ka mahele, ka Holomua me ka like ana - ka hōʻemiʻana geometric Holomua. Ano he kumu hoʻohālike o ia mea, ua piha ma lalo nei.
Laʻana: he 1 = 6, Q = 1/3 - he 1 mea oi o kekahi, Q - emi.
A laila, hiki ke kākau i ke kaʻina o nā helu like penei:
6 2 2/3 ... - kekahi hehee ai hou hehee wale kēia mau mea, he 3 manawa.
- Alternating. Inā Q <0, na hoailona o ka helu o ke kaʻina alternating mau nānā 'ole o ka 1, a me na kumu o kekahi mahuahua a emi.
Laʻana: he 1 = -3, Q = -2 - i nā emi mai o 'Aʻohe.
A laila, he kaʻina o nā huahelu hiki ke palapalaia e like me:
3, 6, -12, 24, ...
haʻilula
No ka pono ana, he nui na geometric Holomua o na nā papakuhikuhi:
- Haʻilula Z-la manawa. Ua apono 'i ka i ka ho omaulia ana o ka hehee ai i loko o kekahi mau' helu me ka helu ana i ka mua helu.
Laʻana: Q = 3, he = 1 4. koi 'ia e hoʻomaulia i ka ha o ka hehee ai Holomua.
Pāʻoihana: He = 4 4 3 · 4-1 · 3 = 4 3 = 4 · 27 = 108.
- I ka huina o na kumu mua, nona ka helu mea like i Z. Ua apono 'i ka i ka ho omaulia ana o ka huina o nā kumu i loko o ke kaʻina i ka Z kauoha aupuni.
≠ 0, penei, Q mea ole 1 - (Q 1) No ka mea, (1- Q) mea i loko o ka denominator, laila.
'Ōlelo Aʻo: ina Q = 1, alaila, o ka Holomua e ua poe i ka helu o endlessly hou i ka helu.
Huina exponentially examples: he 1 = 2, Q = -2. Ho omaulia S 5.
Pāʻoihana: S 5 = 22 - i ka ho omaulia haʻilula.
- Dala ina | Q | <1 a me ka wā Z mālama i ka infinity.
Laʻana: he 1 = 2, Q = 0.5. E huli i ka huina.
Pāʻoihana: S Z = 2 m = 4
Inā mākou e huli i ka huina o kekahi mau hoa o ka manual, oe e ike i ka mea, ua nō i hana i ka eha.
S Z = + 1 + 2 0.5 + 0.25 + 0,125 + 0.0625 = 3.9375 4
Kekahi mau waiwai:
- A ano waiwai. Inā ke kēiaʻano Ua paa no kekahi Z, laila, hāʻawiʻia mai i ka laulā moʻo - he geometric Holomua:
he Z 2 = A Z -1 · A Z + 1
- Ua mea i ka huinahalike o kekahi helu o exponentially ma ka mea o ka hou o na mika pāhoʻonui lua o ka helu'ē aʻeʻelua i loko o kekahi ia lalani, ina ka mea, e equidistant mai ka hehee ai.
2 He Z = ka Z - Halau 2 + he Z + Halau 2 kahi, t - o ka mamao ma waena o kēia mau helu.
- Na kumu mua oko ma Q manawa.
- Nā logarithms o na kumu o ka Holomua like pono hana i ka Holomua, akā, ka makemakika, i mea, kela mea keia mea o lakou i oi ma mua o ka mea mua kekahi ma kekahi mau helu.
Ano he kumu hoʻohālike o kekahi panina pilikia
maopopo i ka maikaʻi i ka mea a ka geometric Holomua, a me ka hooholo ana examples no ka papa 9 hiki ke kōkua.
- Hua'ōlelo a me nā kumu: he 1 = 3, he 3 = 48. E huli i nā Q.
Pāʻoihana: kēlā ka mea i hahai ana ka mea mamuli o kekahi hehee ai i oi ma mua o ka mua Q manawa. He mea pono i ka hoike i kekahi mau kumu ma'ē aʻe Via denominator.
Nolaila, he 3 = Q 2 · ka 1
I ka hookomoia nā nīnau = 4
- Nā kūlana: he 2 = 6, he = 3 12. hoʻomaulia S 6.
Pāʻoihana: No ka hana i kēia, ka mea, ke kala e loaʻa Q, ka mua a me ka hehee ai ae pani i loko o ka haʻilula.
he 3 = Q · he 2, nolaila, Q = 2
he 2 = Q · A 1, no laila, he = 1 3
S = 6 189
- · A 1 = 10, Q = -2. E huli i ka ha o ka hehee ai o ka Holomua.
Pāʻoihana: ka mea, Ua nui ia ka hoike i ka ha o ka hehee ai ma ka mua, a ma ka denominator.
4 He 3 = Q · i = 1 -80
Palapala noi kekahi laʻana:
- Bank Client i ka pilina o ka huina o 10,000 rubles, ma lalo i kēlā me kēia makahiki i ka Client a hiki i ke poʻo kumu a mea dala e e hoʻohuiʻia 6% o ka mea nae. Pehea ka nui o ke kālā i loko o ka mooolelo ma hope o 4 makahiki?
Pāʻoihana: ka loiloi mua dala like i 10 tausani rubles. No laila, i ka makahiki ma hope o nā waihona kālā i loko o ka buke, e ia i ka huina like i 10000 + 10000 = 10000 · 0,06 · 1,06
Alaila, o ka huina ma ka buke a hiki ma hope o kekahi makahiki, e e kaheaia like penei:
(10000 · 1,06) · 10000 · 0,06 + 1,06 = 1,06 · 1,06 · 10000
Ia mea, kēlā me kēia makahiki i ka nui mahuahua i 1,06 manawa. Nolaila, e imi i ka helu o ka mooolelo ma hope o 4 makahiki, ka mea, ke kala i ka imi i ka ha o ka hehee ai Holomua, a ua haawiia mai mua hehee ai like i 10 tausani, a me ka denominator like me 1,06.
S = 1,06 · 1,06 · 1,06 · 1,06 · 10000 = 12625
Ano he kumu hoʻohālike o ka pilikia i loko o ka computation o ka huina o ka:
Ma nā pilikia ka hoʻohana geometric Holomua. An laʻana o loaa i ka huina i ke kau like penei:
he 1 = 4, Q = 2, ho omaulia S 5.
Pāʻoihana: a pau ka mea e pono ikepili no ka i ka ho omaulia i ike, wale panai ia i loko o ka haʻilula.
S 5 = 124
- he 2 = 6, he = 3 18. e huli i ka huina o ka mua eono hehee wale.
pāʻoihana:
Ka Geom. i ka holomua o kēlā me kēia hehee ai o ke kakahiaka nui ma mua o ka mua Q manawa,ʻo ia hoʻi, e hoʻomaulia i ke dala e pono ai, e ike i ka hehee ai he 1 a me ka denominator Q.
he 2 · Q = he 3
nā nīnau = 3
Like me, ka pono, e huli i ke 1, he 2 a me ka ike ana Q.
he 1 · Q = He 2
he 1 = 2
A laila ka mea, ke kala, e panai i ka ikeʻikepili i loko o ka haʻilula dala.
S 6 = 728.
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