Difference: FamousSeries (1 vs. 5)

Revision 52017-10-18 - SteveGaarder

Line: 1 to 1
 
META TOPICPARENT name="InfiniteSeriesSynopsis"

Famous Series

Line: 11 to 11
 
Changed:
<
<
Error during latex2img:
ERROR: problems during latex
INPUT:
\documentclass[fleqn,12pt]{article}
\usepackage{amsmath}
\usepackage[normal]{xcolor}
\setlength{\mathindent}{0cm}
\definecolor{teal}{rgb}{0,0.5,0.5}
\definecolor{navy}{rgb}{0,0,0.5}
\definecolor{aqua}{rgb}{0,1,1}
\definecolor{lime}{rgb}{0,1,0}
\definecolor{maroon}{rgb}{0.5,0,0}
\definecolor{silver}{gray}{0.75}
\usepackage{latexsym}
\begin{document}
\pagestyle{empty}
\pagecolor{white}
{
\color{black}
\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*}
}
\clearpage
\end{document}
STDERR:
This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013)
 restricted \write18 enabled.
entering extended mode
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Babel  and hyphenation patterns for english, dumylang, nohyphenation, lo
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Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
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(/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo))
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For additional information on amsmath, use the `?' option.
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No file aOUtVyFEAf.aux.
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! Missing } inserted.
 
                }
l.17 ...t; 1$ } \end{array} \right.\end{multline*}
                                                  
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 }
                 
l.17 ...t; 1$ } \end{array} \right.\end{multline*}
                                                  
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                }
l.17 ...t; 1$ } \end{array} \right.\end{multline*}
                                                  
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 }
                 
l.17 ...t; 1$ } \end{array} \right.\end{multline*}
                                                  
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                }
l.17 ...t; 1$ } \end{array} \right.\end{multline*}
                                                  
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 }
                 
l.17 ...t; 1$ } \end{array} \right.\end{multline*}
                                                  
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                }
l.17 ...t; 1$ } \end{array} \right.\end{multline*}
                                                  
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 }
                 
l.17 ...t; 1$ } \end{array} \right.\end{multline*}
                                                  
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 }
                 
l.17 ...t; 1$ } \end{array} \right.\end{multline*}
                                                  
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                }
l.17 ...t; 1$ } \end{array} \right.\end{multline*}
                                                  
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 }
                 
l.17 ...t; 1$ } \end{array} \right.\end{multline*}
                                                  
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                }
l.17 ...t; 1$ } \end{array} \right.\end{multline*}
                                                  
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 }
                 
l.17 ...t; 1$ } \end{array} \right.\end{multline*}
                                                  
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                }
l.17 ...t; 1$ } \end{array} \right.\end{multline*}
                                                  
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 }
                 
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                }
l.17 ...t; 1$ } \end{array} \right.\end{multline*}
                                                  
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 }
                 
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 }
                 
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                }
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 }
                 
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 }
                 
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 }
                 
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 }
                 
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                }
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 }
                 
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 }
                 
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 }
                 
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 }
                 
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 }
                 
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 }
                 
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 }
                 
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(That makes 100 errors; please try again.)
No pages of output.
Transcript written on aOUtVyFEAf.log.
>
>
 

P-Series

Revision 42017-10-17 - SteveGaarder

Line: 1 to 1
 
META TOPICPARENT name="InfiniteSeriesSynopsis"

Famous Series

Added:
>
>
 
Line: 7 to 8
 

Geometric Series

Added:
>
>
 
Changed:
<
<
>
>
Error during latex2img:
ERROR: problems during latex
INPUT:
\documentclass[fleqn,12pt]{article}
\usepackage{amsmath}
\usepackage[normal]{xcolor}
\setlength{\mathindent}{0cm}
\definecolor{teal}{rgb}{0,0.5,0.5}
\definecolor{navy}{rgb}{0,0,0.5}
\definecolor{aqua}{rgb}{0,1,1}
\definecolor{lime}{rgb}{0,1,0}
\definecolor{maroon}{rgb}{0.5,0,0}
\definecolor{silver}{gray}{0.75}
\usepackage{latexsym}
\begin{document}
\pagestyle{empty}
\pagecolor{white}
{
\color{black}
\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*}
}
\clearpage
\end{document}
STDERR:
This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013)
 restricted \write18 enabled.
entering extended mode
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LaTeX2e <2011/06/27>
Babel  and hyphenation patterns for english, dumylang, nohyphenation, lo
aded.
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Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
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(/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo))
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?' option.
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(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty))
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(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty))
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No file b8acMynFxr.aux.
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! Missing } inserted.
 
                }
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l.17 ...t; 1$ } \end{array} \right.\end{multline*}
                                                  
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(That makes 100 errors; please try again.)
No pages of output.
Transcript written on b8acMynFxr.log.
 

P-Series

Line: 70 to 80
 

Changed:
<
<
  • you can arrive at this relation by integrating a Geometric Series in -t2 term-by-term.
>
>
  • you can arrive at this relation by integrating a Geometric Series in -t2 term-by-term.
  More... Close
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Revision 32008-11-18 - DickFurnas

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META TOPICPARENT name="InfiniteSeriesSynopsis"

Famous Series

Revision 22008-11-17 - DickFurnas

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META TOPICPARENT name="InfiniteSeriesSynopsis"

Famous Series

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Geometric Series

Changed:
<
<
  • if converges with sum
  • if diverges
>
>

 

P-Series

Changed:
<
<
  • for diverges
>
>

 

Harmonic Series

  • diverges
Changed:
<
<
>
>
 
  • 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.
Changed:
<
<
>
>
 

Exponential

Changed:
<
<
  • converges
>
>

 
Changed:
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<
where
>
>

where

 

Sin

Changed:
<
<
  • converges
>
>

 

Cos

Changed:
<
<
  • converges
>
>
 

ln (1+x)

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

arctan (x)

>
>
  • if x=-1 , i.e. ln(1+(-1)) = ln(0) , this is the negative of the Harmonic Series which diverges toward -∞

arctan (x)

 
Changed:
<
<
  • you can arrive at this relation by integrating a Geometric Series in -t^2 term-by-term.
>
>
  • you can arrive at this relation by integrating a Geometric Series in -t2 term-by-term.
  More... Close
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Changed:
<
<
>
>
 
Changed:
<
<
>
>
 
Changed:
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<
>
>
 
Changed:
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<
>
>
 
Changed:
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<
>
>
 
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Revision 12008-11-16 - DickFurnas

Line: 1 to 1
Added:
>
>
META TOPICPARENT name="InfiniteSeriesSynopsis"

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.
More... Close
<--/twistyPlugin twikiMakeVisibleInline-->

<--/twistyPlugin-->
  • 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.
More... Close
<--/twistyPlugin twikiMakeVisibleInline-->

<--/twistyPlugin-->

-- DickFurnas - 16 Nov 2008

 
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