Difference: FamousSeries (4 vs. 5)

Revision 52017-10-18 - SteveGaarder

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META TOPICPARENT name="InfiniteSeriesSynopsis"

Famous Series

Geometric Series

Changed:
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\begin{multline*}\displaystyle \left \{ \begin{array}{l} \mbox{ \small $=\frac{1}{1-x}$ if $|x| < 1$ } \\ \mbox{ \small diverges if $|x| > 1$ } \end{array} \right.\end{multline*}
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(That makes 100 errors; please try again.)
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Transcript written on pTQldAphXs.log.
>
>
 

P-Series

Harmonic Series

  • diverges
  • this is a special case of the P-Series for P=1

Alternating Harmonic Series

  • converges to ln(1+1) = ln(2) using series for ln(1+x) below.

Exponential

where

Sin

Cos

ln (1+x)

  • you can arrive at this relation by integrating a Geometric Series in -t term-by-term.
More... Close
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  • if x=-1 , i.e. ln(1+(-1)) = ln(0) , this is the negative of the Harmonic Series which diverges toward -∞

arctan (x)

  • you can arrive at this relation by integrating a Geometric Series in -t2 term-by-term.
More... Close
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-- DickFurnas - 16 Nov 2008 \ No newline at end of file

 
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