Famous Series

Geometric Series

  • if converges with sum
  • if diverges

P-Series

  • for diverges

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

  • converges

where

Sin

  • converges

Cos

  • converges

ln (1+x)

  • you can arrive at this relation by integrating a Geometric Series in -t term-by-term.
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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 -&infty;

arctan (x)

  • you can arrive at this relation by integrating a Geometric Series in -t^2 term-by-term.
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-- DickFurnas - 16 Nov 2008

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Topic revision: r1 - 2008-11-16 - 22:05:11 - DickFurnas
 
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