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Yuav ua li cas koj qhia yog hais tias muaj nuj nqi converges los yog diverges?
Yuav ua li cas koj qhia yog hais tias muaj nuj nqi converges los yog diverges?

Video: Yuav ua li cas koj qhia yog hais tias muaj nuj nqi converges los yog diverges?

Video: Yuav ua li cas koj qhia yog hais tias muaj nuj nqi converges los yog diverges?
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Yog koj muaj ib tug series yog me dua ib convergent benchmark series, ces koj series yuav tsum kuj sib hloov . Yog tus qauv ntsuas sib hloov , koj series sib hloov ; thiab yog tus qauv ntsuas sib txawv , koj series sib txawv . Thiab yog koj cov series yog loj dua ib tug sib txawv benchmark series, ces koj series yuav tsum kuj sib txawv.

Tsis tas li ntawd, ua li cas koj thiaj paub yog tias qhov kev txwv converges lossis diverges?

Koj tuaj yeem sau tag nrho nws hauv ib qho theorem: Yog qhov degree ntawm tus lej yog tib yam li qhov degree ntawm tus lej, ces tus sib sib zog nqus rau qhov sib piv ntawm cov thawj coefficients (4/3 hauv qhov piv txwv); yog tus denominator muaj qib siab dua, ces tus sib sib zog nqus rau 0; yog tus lej muaj qib siab dua, Ib sab saum toj, vim li cas 1 n / 2 converge thiab diverge? Los ntawm kev txuas ntxiv hauv li no, koj tuaj yeem saib cov series Σ1 / raws li qhov sib npaug ntawm ntau qhov "pab pawg," tag nrho nrog tus nqi ntau dua. 1 / 2 . Yog li lub series sib txawv , vim yog koj ntxiv 1 / 2 lub sij hawm txaus, cov nyiaj yuav nws thiaj li tau loj npaum li koj nyiam. Cia peb sim nrhiav cov lej no siv lwm cov koob.

Tsuas yog li ntawd, puas yog 1/2 n converge lossis diverge?

Qhov suav ntawm 1/2 ^ n sib , yog li 3 zaug kuj sib hloov . Raws li qhov sib npaug ntawm 3 sib txawv , thiab sum ntawm 1/2 ^ n sib , cov series sib txawv . Koj yuav tsum ceev faj ntawm no, txawm li cas los xij: yog tias koj tau txais ib qho ntawm ob sib txawv series, qee zaus lawv yuav tso tseg ib leeg tawm thiab qhov tshwm sim yuav sib hloov.

Yuav ua li cas koj qhia yog hais tias ib theem zuj zus yog bounded?

Yog hais tias qhov sib lawv liag yog ob qho tib si bounded hauv qab no thiab bounded saum toj no peb hu ua sequence bounded

  1. Nco ntsoov tias nyob rau hauv thiaj li yuav kom ib tug sequence kom nce los yog txo nws yuav tsum tau nce / txo rau txhua txhua n.
  2. Ib ntus yog bounded hauv qab no yog tias peb tuaj yeem pom tus lej m xws li m≤an m ≤ a n rau txhua n.

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