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III. Potensrækker – 2. Talfølger og rækker 278 og er da divergent. 2.29. Nyttige regler 8 Sætning (Regneregler) ☞ [S] 8.2 Series (i) ∞ ∞ can = c (ii) (iii) n=1 n=1 ∞ ∞ (an + bn) = n=1 n=1 ∞ ∞ (an − bn) = n=1 n=1 an an + an − 2.30. Opgave ☞ [S] 8.2 Series Øvelse 28 Undersøg rækken ∞ ln( n n + 1 ) n=1 ∞ n=1 ∞ n=1 Ledene konvergerer ln( n ) → ln(1) = 0 for n + 1 n → ∞ så divergenstesten giver os intet. bn bn
III. Potensrækker – 2. Talfølger og rækker 279 2.31. Opgave Øvelse 28 - fortsat Om afsnitssummen ☞ [S] 8.2 Series sn = ln( 1 n ) + ln(2 ) + · · · + ln( 2 3 n + 1 ) = ln( 1 2 n · · · 2 3 n + 1 ) 1 = ln( n + 1 ) gælder sn → −∞ for n → ∞ 2.32. Opgave Øvelse 28 - fortsat ☞ [S] 8.2 Series Altså er rækken ∞ ln( n n + 1 ) divergent. Men det går langsomt n=1 s 10 6 ≈ ln(10 −6 ) ≈ −14
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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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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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