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III. Potensrækker – 2. Talfølger og rækker 276 Rækken er divergent. 1 − 2 + 3 − 4 + 5 − 6 + ... 2.25. Divergent med forsvindende led ☞ [S] 8.2 Series Eksempel 7 (Paspå) Den harmoniske række har led Men rækken er divergent. ∞ n=1 1 n 1 → 0 når n → ∞ n 2.26. Divergent med forsvindende led ☞ [S] 8.2 Series Eksempel 7 (Paspå) - fortsat Afsnitssummen 1 1 1 s2n =1 + + (1 + ) + (1 + · · · + ) 1 21 3 22 5 23 + · · · + ≥1 + 1 2 1 2n−1 1 + · · · + + 1 2n 1 1 + 2 · + 4 · 1 22 2 2 n 3 + · · · + 2n−1 1
III. Potensrækker – 2. Talfølger og rækker 277 =1 + n 2 giver en divergent følge. 2.27. Kriterie for divergens ☞ [S] 8.2 Series 7 Sætning Hvis limn→∞ an ikke eksisterer eller limn→∞ an = 0, så er rœkken ∞ divergent. Bevis Omformuler Sætning 6. n=1 2.28. Divergente rækker Eksempel ☞ [S] 8.2 Series Rækken ∞ (1 − 1 n ) har led som konvergerer n=1 an an = 1 − 1 → 1 for n → ∞ n
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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0-række/søjle, 423 n-te afsnitssu
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