Yuav ua li cas koj paub yog hais tias lub hwj chim series converges?
Yuav ua li cas koj paub yog hais tias lub hwj chim series converges?

Video: Yuav ua li cas koj paub yog hais tias lub hwj chim series converges?

Video: Yuav ua li cas koj paub yog hais tias lub hwj chim series converges?
Video: Yuav ua cas thiaj paub tias "Nws Hlub Koj" 2024, Kaum ib hlis
Anonim

Cov txiaj ntsig ntawm geometric series ua yeeb yam uas ob lub ntsiab lus yog sib npaug. Ob qho kev qhia tsis sib npaug; qhov tseeb, cov series ntawm txoj cai diverges, los ntawm Zero Limit Test. Koj tuaj yeem siv qhov Kev Ntsuas Ntsuas (thiab qee zaum, Kev Xeem Hauv paus) rau txiav txim cov nqi uas a lub zog series converges.

Ua raws li qhov kev pom no, koj ua li cas ntsuas lub hwj chim rau kev sib koom ua ke?

Txoj kev los txiav txim kev sib koom ua ke ntawm cov ntsiab lus no tsuas yog ntsaws rau hauv qhov qub lub zog series thiab saib seb cov series converges los yog diverges siv ib yam xeem tsim nyog. Qhov no series yog divergent los ntawm Divergence Kuaj vim limn →∞n=∞≠0 lim n → ∞ ? n = ∞ ≠ 0.

Ib sab saum toj no, puas yog 1 N convergent lossis divergent? = 1 ib sib hloov los yog sib txawv. = 1 ib converge. = 1 ib sib txawv.

Kuj Paub, lub caij nyoog ntawm convergence ntawm lub hwj chim series yog dab tsi?

Piv txwv ua haujlwm: interval ntawm convergence . Cov interval ntawm converges ntawm lub hwj chim series yog cov lub sijhawm ntawm input qhov tseem ceeb uas cov series converges.

Nws txhais li cas thaum ib tug series converges?

A series uas sib hloov muaj qhov txwv tsis pub dhau, uas yog tus lej uas tau mus txog. A series uas diverg txhais tau tias ob qho tib si cov nyiaj ib nrab tsis muaj kev txwv lossis mus txog qhov kawg. Qhov sib txawv yog qhov loj ntawm qhov sib piv. Yog |r| <1, tom qab ntawd series yuav sib hloov.

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