Video: Nws txhais li cas rau qhov infinite series los sib sau ua ke?
2024 Tus sau: Miles Stephen | [email protected]. Kawg hloov kho: 2023-12-15 23:36
Muab ib infinite sequence ntu partial sum S yog cov sum ntawm thawj n cov ntsiab lus ntawm cov ib ntus . Ntawd yog, A series yog convergent yog tias ib ntus ntawm nws cov sums ib nrab tends mus rau ib tug txwv; uas txhais tau tias tias cov nyiaj ib nrab tau los ze zog thiab ze rau tus lej muab thaum tus lej ntawm lawv cov ntsiab lus nce.
Raws li txoj cai, vim li cas ib qho kev sib tw tsis kawg ua ke?
A series uas sib hloov muaj qhov txwv tsis pub dhau, uas yog tus lej uas tau mus txog. A series uas diverges txhais tau hais tias ib nrab cov nyiaj tau los tsis muaj kev txwv lossis mus kom ze tsis kawg . Qhov sib txawv yog qhov loj ntawm qhov sib piv. Yog |r| <1, tom qab ntawd series yuav sib hloov.
Tsis tas li ntawd, nws txhais li cas rau qhov zoo series mus sib sau ua ke? Cov zoo series yog convergent , if and only if, the ib ntus ntawm ib nrab sums yog ciam teb; uas yog , muaj ib tug lej M > 0 li ntawd., rau tej. Qhov no tshwm sim muaj ntau qhov cuam tshuam. Piv txwv li, peb muaj cov txiaj ntsig hauv qab no (hu ua Qhov Kev Ntsuas Kev Sib Piv Basic):
Kuj paub, ua li cas koj paub yog tias ib qho infinite series converges?
converge Yog a series muaj qhov txwv, thiab qhov txwv muaj, tus series converges . sib txawv Yog a series tsis muaj qhov txwv, lossis txwv tsis pub tsis kawg , tiam series yog divergent. sib txawv Yog a series tsis muaj qhov txwv, lossis txwv tsis pub tsis kawg , tiam series sib txawv.
Nws txhais li cas rau qhov txwv kom sib koom ua ke?
Converge yog ib tug verb uas siv txwv , sequences, series, thiab integrals. Lo lus diverge yog siv rau qhov tsis zoo ntawm nws. A txwv converges yog nws muaj, uas yog, yog hais tias nws muaj ib tug finite nqi. Nws diverges yog tias nws tsis muaj.
Pom zoo:
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