Qhov sib lawv liag hauv qhov piv txwv tsis yog monotonic tab sis nws ua ke. Nco ntsoov tias peb tuaj yeem ua ntau qhov sib txawv ntawm qhov theorem no. Yog hais tias {ib} yog bounded saum toj no thiab nce ces nws converges thiab zoo li yog tias {ib} yog bounded hauv qab no thiab txo ces nws converges.
Puas yog tag nrho cov monotonic sequences convergent?
ib ntus (a ) yog monotonic nce yog tias a +1≥ a rau tag nrho n ∈ N. Cov kab ke yog nruj me ntsis monotonic nce yog tias peb muaj > hauv lub ntsiab lus. Monotonic txo sequences raug txhais zoo sib xws. A bounded monotonic nce ib theem yog convergent.
Puas yog cov koob yuav tsum yog monotonic los sib sau ua ke?
Tsis yog txhua qhov kev sib tw, zoo li (−1)n, sib koom ua ke, tab sis yog tias peb paub tias qhov kev sib tw bounded yog monotone, qhov no yuav hloov. Yog tias ib qho ≥ ib + 1 rau tag nrho n ∈ N. Ib ntu yog monotone yog tias nws nce lossis qis. thiab bounded, ces nws converges.
Yuav ua li cas tsis muaj bounded sequence yuav convergent?
Yog li kev sib tw tsis tuaj yeem sib koom ua ke.
Nws txhais li cas yog tias ib ntus tsis yog monotonic?
Yog tias ib ntus qee zaum nce thiab qee zaum qis dua thiab yog li tsis muaj kev coj ua zoo ib yam, nws txhais tau tias qhov sib lawv liag tsis yog monotonic. Nyob rau hauv lwm yam lus, ib tug tsis-monotonic ib theem zuj zus rau ib feem ntawm qhov sib lawv liag thiab txo rau lwm tus.
