Yog tias qhov no ntawm cov nyiaj ib nrab s n s_n sn converges li n → ∞ n\to\infty n→∞ (yog tias peb tau tus nqi tiag tiag rau s), ces peb tuaj yeem hais tias cov koob ntawm cov nyiaj ib nrab converges, uas tso cai rau peb los xaus tias lub koob yees duab telescoping a n a_n ib kuj converges.
Dab tsi ua rau telescoping series diverge?
vim tshem tawm cov lus nyob ib sab. Yog li, cov lej ntawm cov koob, uas yog qhov txwv ntawm cov nyiaj ib nrab, yog 1. thiab ib qho kev suav tsis kawg nrog lub sijhawm tas mus li diverges.
Yuav ua li cas rau kev sib koom ua ke?
Dua, raws li tau sau tseg saum toj no, tag nrho cov theorem no yog muab rau peb qhov yuav tsum tau ua kom muaj kev sib koom ua ke. Yuav kom ib tug series converge lub series cov nqe lus yuav tsum mus rau xoom nyob rau hauv txwv Yog hais tias cov ntsiab lus series tsis mus rau xoom nyob rau hauv qhov txwv ces tsis muaj txoj kev uas series yuav converge vim qhov no yuav ua txhaum lub theorem.
Yuav ua li cas koj thiaj paub yog hais tias ib ntus converge?
Yog peb hais tias ib ntu sib txuas, txhais tau hais tias qhov txwv ntawm kab ke muaj xws li n → ∞ n\to\infty n→∞Yog qhov txwv ntawm kab ke raws li n → ∞ n\to\infty n→∞ tsis muaj nyob, peb hais tias qhov sib lawv liag sib txawv. Ib ntu ib txwm yog converges lossis diverges, tsis muaj lwm txoj kev xaiv.
Yuav ua li cas koj paub yog nws convergent los yog divergent?
converge Yog ib koob muaj qhov txwv, thiab qhov txwv muaj, cov koob sib txuas. divergent Yog hais tias ib tug series tsis muaj qhov txwv, los yog qhov txwv yog infinity, ces cov series yog divergent. divergesYog hais tias ib tug series tsis muaj qhov txwv, los yog qhov txwv yog infinity, ces cov series diverges.
