Haereraa āhuahanga. TAUIRA ki te whakatau

Fakakaukau ki he rarangi.

7 28 112 448 1792 ...

Tino mārama whakaatu e te uara o tetahi o ona āhuatanga nui atu i te mua rite wha ngā wā. Na, tenei raupapa ko te haereraa.

haereraa āhuahanga i huaina raupapa mure o tau, te āhuatanga matua o te mea e whiwhi i te maha e whai ake te i te i runga i te whakanuia e etahi tau tino. Ua faaite tenei e te tātai e whai ake.

_{he z +1 = te q z ·} , te wahi z - maha o te huānga tīpakohia.

Fakatatau ki ai, z ∈ N.

He wa ka ako te kura te ahunga whakamua āhuahanga - kōeke 9. Tauira ka tokoni ke mahino te ariā:

0.25 0.125 0.0625 ...

18 February 6 ...

I runga i tenei tātai, kia kitea ai te ahunga whakamua o te tauraro e whai ake:

e kore e taea e kore q, ranei b _z kia kore. Ano, ia o nga āhuatanga o te raupapa o ngā tau e kore e waiho haereraa kore.

Fakatatau ki ai, ki te kite i te maha i muri o te tau, kia tini te muri i te q.

Hei tautuhi i tēnei ahunga whakamua, me whakapūtā koe te huānga tuatahi o taua mea, me te tauraro. I muri i taua ko reira taea ki te kitea e tetahi o nga mema o e whai ake nei me ratou nui.

momo

Tei runga i te q me te _1, kei te wehea tenei haereraa ki te maha momo:

• Ki te he _1, me q he nui ake i te kotahi, ka he raupapa - te whakanui ake ki ia huānga ngā o te haereraa āhuahanga. Tauira e ngā ona i raro.

Tauira: he ₁ = 3, q = 2 - nui atu i kotahitanga, tawhā e rua.

Na e taea te tuhituhi i te raupapa o ngā tau rite:

3 6 12 24 48 ...

• Ki te | q | iti iho i te kotahi, arā, ko reira rite ki te whakareatanga i te wehenga, te haereraa ki tikanga rite - whakaiti haereraa āhuahanga. Tauira e ngā ona i raro.

Tauira: he ₁ = 6, q = 1/3 - he nui ake i te kotahi i te _1, q - iti.

Na e taea te tuhituhi i te raupapa o ngā tau e whai ake:

Pipiri 2 2/3 ... - tetahi huānga ake huānga e whai ake i te reira, ko te 3 ngā wā.

• Tauutuutu. Ki te q <0, nga tohu o nga tau o te tauutuutu raupapa tonu ahakoa o te _1, me nga mea timatanga o tetahi hua heke ranei.

Tauira: he ₁ = -3, q = -2 - he rua iti iho i te kore.

Na e taea te tuhituhi i te raupapa o ngā tau rite:

3, 6, -12, 24, ...

tātai

Hoki te whakamahi watea, i reira e maha ahu āhuahanga o te tātai:

• Tātai z-th wā. āhei te reira i te tātaitanga o te huānga i roto i te tau motuhake, kahore te tātai i te tau o mua.

Tauira: q = 3, he = ₁ 4. hiahiatia ki te tātai i te haereraa huānga tuawha.

Rongoā: he = ₄ 4 3 · ^4-1 · 3 = 4 ³ = 4 · 27 = 108.

• He rite ki te moni o te āhuatanga tuatahi, tona maha z. āhei te reira i te tātaitanga o te moni o nga āhuatanga katoa i roto i te raupapa ki te urutomo _z.

≠ 0, te kupu, e kore he q 1 - (q 1) Mai (1- q) kei roto i te tauraro, ka.

Tuhipoka: ki te q = 1, na te haereraa e kua kanohi he maha o oku taengata tukurua te tau.

Te nui ē tauira: he ₁ = 2, q = -2. Tātaihia S _5.

Rongoā: S ₅ = 22 - tātaitanga tātai.

• Te nui ki te | q | <1 a ka whangai z ki mutu-.

Tauira: he ₁ = _2, q = 0.5. Kimihia te moni.

Rongoā: S _z = 2 x = 4

Ki te tātai tatou te moni o te maha ngā mema o te buka haapiiraa, e kite koe i e te pono tukua reira ki wha.

S _z = + 1 + 2 0.5 + 0.25 + 0,125 + 0.0625 = 3.9375 4

Ētahi āhuatanga:

• He taonga āhuatanga. Ki te te huru e whai ake nei mau te reira mo tetahi z, ka homai he raupapa tau - he haereraa āhuahanga:

he _z ² = He _{z -1} · He _{z + 1}

• Ko hoki reira ko ē te tapawha o tetahi tatau i te tikanga o tua o te tapawhā o te tahi atu tau e rua i roto i tetahi rarangi i homai, ki te he equidistant i te huānga ratou.

² te _z = he _{z - t} ² ₊ te _z + _t ² wahi t - te tawhiti i waenganui i enei tau.

• rerekē te āhuatanga i ngā wā q.
• Ko te taupū kōaro o te āhuatanga o te ahunga whakamua me te hanga i te ahunga whakamua, ko te tauhanga, e ko, ia nui atu i te kotahi o mua o ratou e te maha tetahi.

Tauira o etahi raruraru puāwaitanga

Hei mahino pai aha te haereraa āhuahanga, me te tauira whakatau mō te kōeke 9 taea te āwhina.

• Ngā me tikanga: he ₁ = 3, he ₃ = 48. Rapu q.

Rongoā: ia huānga ngā i roto i te neke atu i te q o mua wā. He mea tika ki te whakapuaki i te tahi mau huānga i roto i te tahi atu mā tauraro.

Nā tēnei, he ₃ = q ² · he ₁

A, no te whakakapi q = 4

• Tikanga: he ₂ = 6, he = ₃ 12. Tātaihia S _6.

Rongoā: Ki te mahi i tenei, tatu ki te kitea q, te huānga tuatahi, me te whakakapi ki te tātai.

he ₃ = q · he _2, no reira, q = 2

he ₂ = q · A _1, na he = ₁ 3

S = ₆ 189

• · He ₁ = 10, q = -2. Kimihia te wha o nga huānga o te haereraa.

Rongoā: ko reira nui ki te whakapuaki i te wha o nga huānga i roto i te tuatahi, me te roto i te tauraro.

₄ he ³ = q · he = ₁ -80

tauira Taupānga:

• Kua whai wāhi kiritaki Bank te moni o 10,000 moni, i raro i nei i ia tau i te kiritaki ki te nui tino ka tapiritia 6% o reira ahakoa. Kia pehea te nui te moni kei roto i te pūkete i muri i te 4 tau?

Rongoā: Ko te nui tuatahi rite ki te 10 mano moni. Na, he tau i muri i te haumi i roto i te pūkete, ka hei te nui rite ki te 10000 + 10000 = 10000 · 0,06 · 1,06

Nä, ko te nui i roto i te pūkete noa i muri ka kotahi tau e faaite e whai ake:

(10000 · 1.06) · 10000 · 0.06 + 1.06 = 1.06 · 1.06 · 10000

Ko, i ia tau nui haere te nui ki 1,06 wā. No reira, ki te kitea te maha o te pūkete i muri i te 4 tau, tatu ki te kitea te ahunga whakamua te wha huānga, homai nei huānga tuatahi rite ki te 10 mano, me te tauraro rite ki 1,06.

S = 1,06 · 1,06 · 1,06 · 1,06 · 10000 = 12625

Tauira o ngā raruraru i roto i te tätaitanga o te moni o:

I roto i ngā raruraru mā te whakamahi i haereraa āhuahanga. kia whakaturia ai tētahi tauira o te kimi i te moni e whai ake:

he ₁ = 4, q = 2, tātai S _5.

Rongoā: kua mohiotia nga raraunga e tika ana katoa mo te tātai, te whakauru ia ratou noa ki te tātai.

S ₅ = 124

• he ₂ = 6, he = ₃ 18. Tātaihia te moni o nga āhuatanga tuatahi e ono.

otinga:

Te Geom. te ahunga whakamua o ia huānga o te muri nui atu i te wā q o mua, e ko, ki te tātai i te nui e hiahia ana koe ki te mohio i te huānga he ₁ me te q tauraro.

he ₂ · q = te ₃

q = 3

Oia atoa, ki te hiahia kitea he _1, he _2, me te mohio q.

he ₁ · q = te ₂

he ₁ = 2

A ka tatu ki te whakauru i te raraunga mohiotia ki te nui tātai.

S ₆ = 728.