Video: Dab tsi yog qhov sum ntawm geometric series?
2024 Tus sau: Miles Stephen | [email protected]. Kawg hloov kho: 2023-12-15 23:36
Nyob rau hauv thiaj li yuav infinite Geometric series kom muaj ib sum , qhov sib piv r yuav tsum nyob nruab nrab ntawm −1 thiab 1. Kom pom qhov sum ntawm ib qho infinite Geometric series muaj qhov sib piv nrog tus nqi tiag tiag tsawg dua ib qho, siv tus qauv, S = a11−r, qhov twg a1 yog thawj lub sij hawm thiab r yog qhov sib piv.
Yog li ntawd, yuav ua li cas koj thiaj nrhiav tau cov lej ntawm cov duab geometric?
Rau nrhiav tus lej ntawm ib tug finite Geometric series , siv cov qauv , Sn = a1(1−rn)1−r, r≠1, qhov twg n yog tus lej ntawm nqe lus, a1 yog thawj lub sijhawm thiab r yog qhov sib piv.
Tsis tas li ntawd, tus qauv ntawm geometric kev nce qib yog dab tsi? Hauv lej, a Geometric kev nce qib ( ib ntus ) (tseem tsis raug hu ua a Geometric series ) yog a ib ntus ntawm cov lej xws li cov quotient ntawm ob tus tswv cuab txuas ntxiv ntawm cov ib ntus yog ib qhov tas mus li hu ua qhov sib piv ntawm cov ib ntus . Cov Geometric kev nce qib tuaj yeem sau ua: ar0= a, aw1= ua, ar2,ar3, Ib yam li ntawd ib tug yuav nug, dab tsi yog qhov suav ntawm infinite geometric series?
Ib infinite geometric series yog cov sum ntawm ib infinite geometric sequence . Qhov no series yuav tsis muaj hnub kawg. General daim ntawv ntawm lub infinite geometric series yog a1+a1r+a1r2+a1r3+, qhov twg a1 yog thawj lub sij hawm thiab r yog qhov sib piv. Peb tuaj yeem nrhiav tau sum ntawm tag nrho cov finite Geometric series.
Dab tsi yog tus qauv rau cov lej ntawm geometric kev nce qib?
Geometric Progression Daim ntawv dav dav ntawm GP yog a, ar, ar2,ar3 thiab lwm yam. Lub sijhawm nth ntawm GP series yog T = ar -1, qhov twg a = thawj lub sij hawm thiab r = common ratio = T /T -1) Cov sum ntawm infinite cov nqe lus ntawm GP series S∞= a/(1-r) uas 0<r<1.
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