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Changed:  
< <  Infinite Series: A Synopsis  
> >  Infinite Series: A Synopsis  
Changed:  
< <  Famous SeriesGeometric Series
PSeries
Harmonic Series
Alternating Harmonic Series
Exponential
where Sin
Cos
ln (1+x)
</twistyPlugin twikiMakeVisibleInline>
</twistyPlugin>
arctan (x)
</twistyPlugin twikiMakeVisibleInline>
 
> >  Famous Series
Geometric Series
PSeries
Harmonic Series
Alternating Harmonic Series
Exponential
where Sin
Cos
ln (1+x)
</twistyPlugin twikiMakeVisibleInline>
</twistyPlugin>
arctan (x)
</twistyPlugin twikiMakeVisibleInline>
</twistyPlugin>  
Changed:  
< < 
</twistyPlugin>
Useful Limits  
> >  Useful Limits  
Exponentials
Powers and Roots
Properties of LimitsThe limit of a sum is the sum of the limits:
The limit of a product is the product of the limits:
The limit of a quotient is the quotient of the limits:
Squeeze Theorem:
AKA the "Flyswatter Theorem". Why?
Ratios of PolynomialsThe limiting behavior of the ratio of two polynomials depends on the degree of the polynomials. The polynomial of higher degree "wins". If their degrees are the same, then the limit is the ratio of the leading coefficients.
 
Changed:  
< <  Useful InequalitiesAlways  
> >  Useful Inequalities
Always
Eventually
New Series From Old
Multiply by a constant:
Substitute an expression for x:
Multiply by a power of x:
Integrate:
Differentiate:
 
Changed:  
< < 
Eventually
 
> >  Convergence Tests%INCLUDE{ConvergenceTests]]%  
Changed:  
< <  Tips for Series  
> >  Tips for Series  
 
Changed:  
< < 
 
> > 
 

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Infinite Series: A Synopsis  
Line: 77 to 77  
</> </twistyPlugin>  
Added:  
> >  Useful Limits
Exponentials
Powers and Roots
Properties of LimitsThe limit of a sum is the sum of the limits:
The limit of a product is the product of the limits:
The limit of a quotient is the quotient of the limits:
Squeeze Theorem:
AKA the "Flyswatter Theorem". Why?
Ratios of PolynomialsThe limiting behavior of the ratio of two polynomials depends on the degree of the polynomials. The polynomial of higher degree "wins". If their degrees are the same, then the limit is the ratio of the leading coefficients.
 
Useful InequalitiesAlways 
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Infinite Series: A Synopsis 
Line: 1 to 1  

Infinite Series: A Synopsis  
Line: 78 to 78  
</> </twistyPlugin>
Useful Inequalities  
Changed:  
< <  
> >  Always  
Changed:  
< <  
> > 
Eventually
 
Changed:  
< < 
"Eventually"
for any (!) Remember this when using the Test for Divergence
Tips  
> >  Tips for Series  
 
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{math}\displaystyle n \rarrow \infty\end{math} } \clearpage \end{document} STDERR: This is pdfTeX, Version 3.14159262.51.40.14 (TeX Live 2013) restricted \write18 enabled. entering extended mode (/tmp/HOAHiOfksA/l8yjurz4Mx LaTeX2e <2011/06/27> Babel  
> > 
 
 DickFurnas  21 Oct 2008 
Line: 1 to 1  

Infinite Series: A Synopsis  
Line: 7 to 7  
Famous SeriesGeometric Series  
Changed:  
< <  
> >  
 
Added:  
> >  
PSeries  
Changed:  
< <  
> >  
 
Added:  
> >  
Harmonic Series
 
Added:  
> > 
 
Alternating Harmonic Series  
Changed:  
< < 
 
> > 
 
Exponential
 
Added:  
> >  where  
Sin
 
Line: 38 to 43  
 
Added:  
> > 
</twistyPlugin twikiMakeVisibleInline>
</twistyPlugin>
 
arctan (x)
 
Added:  
> > 
</twistyPlugin twikiMakeVisibleInline>
</twistyPlugin>
Useful Inequalities
"Eventually"
for any (!) Remember this when using the Test for Divergence
Tips
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{math}\displaystyle n \rarrow \infty\end{math} } \clearpage \end{document} STDERR: This is pdfTeX, Version 3.14159262.51.40.14 (TeX Live 2013) restricted \write18 enabled. entering extended mode (/tmp/N9AYVSpl7L/uHSxksgNXc LaTeX2e <2011/06/27> Babel  
 DickFurnas  21 Oct 2008 
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Added:  
> > 
Infinite Series: A Synopsis
Famous SeriesGeometric Series
PSeries
Harmonic Series
Alternating Harmonic Series
Exponential
Sin
Cos
ln (1+x)
arctan (x)
 DickFurnas  21 Oct 2008 