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III. Potensrækker – 2. Talfølger og rækker 274 er konvergent for |r| < 1 med sum Rækken er divergent for øvrige r (a = 0). ∞ n=0 ar n = a 1 − r 2.21. Bevis geometrisk række ☞ [S] 8.2 Series Bevis Afsnitssummen findes som kvotientrække sn = a + ar + ar 2 + · · · + ar n 1 − rn+1 = a 1 − r Så rækken er konvergent for |r| < 1 med sum ∞ n=0 ar n = a 1 − r 2.22. En sum findes ☞ [S] 8.2 Series Eksempel Den geometriske række ∞ 1 2n har r = 1 2 og er konvergent. n=0
III. Potensrækker – 2. Talfølger og rækker 275 Summen findes ∞ n=0 1 1 = 2n 1 − 1 2 2.23. Led forsvinder ☞ [S] 8.2 Series 6 Sætning Hvis rœkken ∞ n=1 an er konvergent, så gœlder Bevis Antag sn → s når n → ∞. når n → ∞. lim n→∞ an = 0 = 2 an = sn − sn−1 → s − s = 0 2.24. Divergente rækker ☞ [S] 8.2 Series Eksempler Den geometriske række ∞ (−1) n = 1 − 1 + 1 − 1 + ... er divergent. n=0
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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Forord "Slides" til forelæsningern
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V. Matricer - 4. Determinanter 419
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Litteratur • Arnold, Ordinary dif
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0-række/søjle, 423 n-te afsnitssu
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Identitetsmatricen, 383 Identitetsm
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