convergeIf ib koob muaj qhov txwv, thiab qhov txwv muaj, cov koob sib txuas. divergentYog hais tias ib tug series tsis muaj qhov txwv, los yog qhov txwv yog infinity, ces cov series yog divergent.
Yuav ua li cas koj thiaj paub yog converge los yog diverge?
Yog tias koj tau txais cov koob uas me dua li qhov sib koom ua ke, ces koj cov koob yuav tsum sib koom ua ke. Yog qhov ntsuas ntsuas sib txuas, koj cov koob sib txuas; thiab yog hais tias tus benchmark diverges, koj series diverges. Thiab yog tias koj cov koob muaj ntau dua li qhov sib txawv ntawm qhov sib txawv, ces koj cov koob yuav tsum sib txawv.
Yuav ua li cas koj thiaj paub yog hais tias ib tug series converges?
Yog hais tias qhov sib lawv liag ib nrab yog ib qho kev sib koom ua ke (piv txwv li nws qhov kev txwv muaj thiab yog qhov kawg) ces cov koob kuj tseem hu ua convergent thiab qhov no yog limn →∞sn=s lim n → ∞ s n=s ces, ∞∑i=1ai=s ∑ i=1 ∞ a i=s.
Puas 1 Ex converge or diverge?
1/(ex) loj dua los yog sib npaug rau 1/(ex+1) (nruab nrab xoom thiab infinite) Improper integral ∫∞01(ex)dx yog convergent thiab nws yog 1 txawm li cas los xij, improper integral ∫∞01 (ex+1)dx is divergent.
Puas 0 diverge lossis converge?
Yog li ntawd, yog tias qhov txwv ntawm n a_n ib yog 0, ces tus lej yuav tsum sib npaug. Teb: Yog, ib qho ntawm thawj yam uas koj kawm txog infinite series yog tias yog hais tias cov nqe lus ntawm cov series tsis mus txog 0, ces cov series tej zaum yuav converging. Qhov no muaj tseeb.
