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Uke 7

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Det er gitt to positive rekker $\\sum\\limits_{n=0}^{\\infty}a_n$ og $\\sum\\limits_{n=0}^{\\infty}b_n$ slik at $a_n\\geq b_n$ for alle $n$. 

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Velg riktige påstander

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Det er gitt en rekke $\\sum\\limits_{n=0}^{\\infty}\\frac{n+1}{2n^2+2}$.

\n

Vi regner ut at $\\lim\\limits_{n\\rightarrow\\infty}\\dfrac{\\frac{n+1}{2n^2+2}}{\\frac{1}{n}}=\\lim\\limits_{n\\rightarrow\\infty}\\dfrac{n^2+n}{2n^2+2}=\\frac{1}{2}$

\n

Videre vet vi at at rekken $\\sum\\limits_{n=0}^{\\infty}\\frac{1}{n}$ divergerer.

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Hva kan vi da si om rekken $\\sum\\limits_{n=0}^{\\infty}\\frac{n+1}{2n^2+2}$?

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Avgjør om rekken er absolutt konvergent, betinget konvergent eller divergent

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$\\sum\\limits_{n=1}^{\\infty}\\frac{(-1)^n}{n}$

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$\\sum\\limits_{n=0}^{\\infty}\\frac{(-1)^n}{(n+1)^2}$

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$\\sum\\limits_{n=1}^{\\infty}\\frac{(-1)^n}{\\sqrt{n}}$

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$\\sum\\limits_{n=2}^{\\infty}(-1)^n\\frac{n}{\\ln{n}}$

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