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III. Potensrækker – 2. Talfølger og rækker 272 Skrives også ∞ n=1 2.17. Afsnitssum ☞ [S] 8.2 Series 2 Definition Rækken ∞ n=1 an har n-te afsnitssum 1 n 2 sn = a1 + · · · + an = Rækken kaldes konvergent, hvis talfølge {sn} er konvergent og i modsat fald divergent. s = limn→∞ sn kaldes rækkens sum og skrives ∞ an = s n=1 2.18. Enkel udregning ☞ [S] 8.2 Series Eksempel 6 Rækken n i=1 ai 1 1 1 + + · · · + + ... 1 · 2 2 · 3 n(n + 1)
III. Potensrækker – 2. Talfølger og rækker 273 har led og afsnitssum an = 1 1 1 = − n(n + 1) n n + 1 sn = 1 − 1 1 1 1 1 1 + − + · · · + − = 1 − 2 2 3 n n + 1 n + 1 2.19. Enkel udregning ☞ [S] 8.2 Series Eksempel 6 - fortsat Afsnitssummen er konvergent Rækken er da konvergent sn = 1 − 1 → 1 når n → ∞ n + 1 ∞ n=1 1 = 1 n(n + 1) 2.20. Geometrisk række ☞ [S] 8.2 Series 4 Sætning (Geometrisk række) Den geometriske række ∞ n=0 ar n = a + ar + ar 2 + ...
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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0-række/søjle, 423 n-te afsnitssu
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