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

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

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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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