grenzwert < Folgen+Grenzwerte < Analysis < Oberstufe < Schule < Mathe < Vorhilfe
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(Frage) beantwortet  | | Datum: | 21:45 Di 16.02.2010 | | Autor: | lalalove |
[mm] c_{n} [/mm] = [mm] \bruch{4n}{2n+1} [/mm] + [mm] (\bruch{1}{10})^{2}
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[mm] \limes_{n\rightarrow\infty}\bruch{4n}{2n+1} [/mm] + [mm] (\bruch{1}{10})^{2}
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= [mm] \limes_{n\rightarrow\infty}\bruch{4}{2+\bruch{1}{n}}+(\bruch{1}{10})^2
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= [mm] \bruch{\limes_{n\rightarrow\infty} 4}{\limes_{n\rightarrow\infty} 2} [/mm] + [mm] \limes_{n\rightarrow\infty} (\bruch{1}{10})^n [/mm] = [mm] \bruch{4}{2} [/mm] +0 = 2
so richtig?
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Hallo lalalove,
> [mm] $c_{n}= \bruch{4n}{2n+1}+ (\bruch{1}{10})^{\red{2}}$
[/mm]
Das soll hier und im weiteren [mm] $\left(\frac{1}{10}\right)^{\red{n}}$ [/mm] heißen , oder?
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> [mm]\limes_{n\rightarrow\infty}\bruch{4n}{2n+1}[/mm] +
> [mm](\bruch{1}{10})^{2}[/mm]
>
> =
> [mm]\limes_{n\rightarrow\infty}\bruch{4}{2+\bruch{1}{n}}+(\bruch{1}{10})^2[/mm]
> = [mm]\bruch{\limes_{n\rightarrow\infty} 4}{\limes_{n\rightarrow\infty} \red{(}2\red{+\frac{1}{n})}}[/mm] + [mm]\limes_{n\rightarrow\infty} (\bruch{1}{10})^n[/mm]
Aha, also doch "hoch n"
> = [mm]\bruch{4}{2}[/mm] +0 = 2 ![[ok]](/images/smileys/ok.gif "[ok]")
>
> so richtig?
Ja, gut so!
LG
schachuzipus
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