Yuav ua li cas yog cov khoom ntawm cov lej lej lej lej lej lej Ib qho lej lej lossis lej lej yogcov lej xws li qhov sib txawv ntawm cov lus sib law liag . Piv txwv li, kab lus 5, 7, 9, 11, 13, 15,… yog ib qho kev ua lej lej nrog qhov sib txawv ntawm 2. https://en.wikipedia.org › wiki › Arithmetic_progression
Kev nce qib lej - Wikipedia
? Ua ntej peb saib cov ntaub ntawv tsis tseem ceeb ntawm ib ntu tas mus li a =a for all n. Peb tam sim ntawd pom tias xws li ib ntus yog bounded; Tsis tas li ntawd xwb, nws yog monotone, uas yog nws tsis txo qis thiab tsis nce.
Puas yog tag nrho cov sequences monotonic?
Peb xav tau cov hauv qab no. Ib ntus (a ) yogmonotonic nce yog tias a +1≥ a rau txhua tus n∈ N. Cov kab ke yog nruj me ntsis monotonic nce yog tias peb muaj > hauv qhov txhais. Monotonic txo cov sequences raug txhais zoo ib yam.
piv txwv monotonic sequence yog dab tsi?
Monotonicity: Cov kab ke sn tau hais kom nce ntxiv yog sn sn + 1 rau tag nrho n 1, i.e., s1 s2 s3 …. … Ib ntu tau hais tias yog monotone yog tias nws nce lossis txo qis. Piv txwv. Cov kab ke n2: 1, 4, 9, 16, 25, 36, 49, … yog nce.
Dab tsi txhais cov kab lus monotonic?
Monotone Sequences. Txhais: Peb hais tias ib ntus (xn) yognce yog xn ≤ xn + 1 rau tag nrho n thiab nruj me ntsis nce yog xn < xn + 1 rau tag nrho n. Ib yam li ntawd, peb txhais cov kev txo qis thiab nruj me ntsis txo cov kab ke. Cov kab ke uas nce lossis txo qis yog hu ua monotone.
Koj ua pov thawj li cas ib ntus yog monotonic?
an≥an+1 rau txhua tus n∈N. Yog {ib} nce lossis txo qis , ces nws hu ua monotone sequence.
Ua pov thawj tias txhua qhov sib txuas hauv qab no yog convergent thiab nrhiav nws txwv.
- a1=1 thiab +1=an+32 rau n≥1.
- a1=√6 and an+1=√an+6 for n≥1.
- an+1=13(2an+1a2n), n≥1, a1>0.
- an+1=12(an+ban), b>0.
