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https://texercises.com/exercise/konvergenzkriterien-iii/
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Exercise:
Konvergiert die folge Reihe? _n^infty fracsqrtn+sqrtn+

Solution:
Zunächst verwet man den Wurzeltrick: a_n fracsqrtn+sqrtn+ fracsqrtn+sqrtn+ fracsqrtn-sqrtn+sqrtn-sqrtn+ fracsqrtn-sqrtn+n-n+sqrtn+-sqrtn Dies erlaubt es Partialmen S_N zu bestimmen: S_ - S_ -+sqrt- sqrt S_ -+sqrt-+sqrt-sqrt sqrt ... S_N -+sqrt-+sqrt-sqrt+...+sqrtN--sqrtN+sqrtN+-sqrtN sqrtN+ Nach Definition kann man so den Limes bestimmen: _n^infty fracsqrtn+sqrtn+ oversettextDef. limlimits_N rightarrow inftyS_N limlimits_N rightarrow inftysqrtN+infty Die Reihe ist somit divergent.
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Exercise:
Konvergiert die folge Reihe? _n^infty fracsqrtn+sqrtn+

Solution:
Zunächst verwet man den Wurzeltrick: a_n fracsqrtn+sqrtn+ fracsqrtn+sqrtn+ fracsqrtn-sqrtn+sqrtn-sqrtn+ fracsqrtn-sqrtn+n-n+sqrtn+-sqrtn Dies erlaubt es Partialmen S_N zu bestimmen: S_ - S_ -+sqrt- sqrt S_ -+sqrt-+sqrt-sqrt sqrt ... S_N -+sqrt-+sqrt-sqrt+...+sqrtN--sqrtN+sqrtN+-sqrtN sqrtN+ Nach Definition kann man so den Limes bestimmen: _n^infty fracsqrtn+sqrtn+ oversettextDef. limlimits_N rightarrow inftyS_N limlimits_N rightarrow inftysqrtN+infty Die Reihe ist somit divergent.
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Series and sequences
Tags
analysis, eth, grenzwert, hs22, konvergenz, limes, reihe
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Difficulty
(2, default)
Points
0 (default)
Language
GER (Deutsch)
Type
Calculative / Quantity
Creator rk
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