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https://texercises.com/exercise/criterio-dellintegrale-e-serie-1/
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Exercise:
Sfruttando il seguente disegno dimostra che la serie armonica _ngeq fracn diverge. center tikzpicturexscaleyscale defa defb defL pgfmathtruncatemacroala+L pgfmathtruncatemacroblb-L draw-thick -- b coordinate x axis noderight x; draw-thick -. -- . coordinate y axis nodeleft y; foreach f in aal...bl pgfmathparse./f pgfmathresult drawfillblue! fpgfmathresult |- x axis -- fpgfmathresult -- f+Lpgfmathresult -- f+Lpgfmathresult |- x axis -- cycle; draw f nodebelow footnotesizef; draw b nodebelow footnotesizeb; drawredthicksmoothsamplesdomain.:b plotx./x; drawcolorred .. node yfracx; tikzpicture center

Solution:
Siccome la funzione fracx è decrescente possiamo dire che _n^infty fracngeq _^inftyfracxdxlnxBig|^infty_+infty.
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Exercise:
Sfruttando il seguente disegno dimostra che la serie armonica _ngeq fracn diverge. center tikzpicturexscaleyscale defa defb defL pgfmathtruncatemacroala+L pgfmathtruncatemacroblb-L draw-thick -- b coordinate x axis noderight x; draw-thick -. -- . coordinate y axis nodeleft y; foreach f in aal...bl pgfmathparse./f pgfmathresult drawfillblue! fpgfmathresult |- x axis -- fpgfmathresult -- f+Lpgfmathresult -- f+Lpgfmathresult |- x axis -- cycle; draw f nodebelow footnotesizef; draw b nodebelow footnotesizeb; drawredthicksmoothsamplesdomain.:b plotx./x; drawcolorred .. node yfracx; tikzpicture center

Solution:
Siccome la funzione fracx è decrescente possiamo dire che _n^infty fracngeq _^inftyfracxdxlnxBig|^infty_+infty.
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Attributes & Decorations
Tags
Calcolo integrale, Criterio dell'integrale e serie
Difficulty
(1, default)
Points
0 (default)
Language
ITA (Italiano)
Type
Calculative / Quantity
Decoration
Content image