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Famous Series
Table of Contents
Famous Series
Geometric Series
P-Series
Harmonic Series
Alternating Harmonic Series
Exponential
Sin
Cos
ln (1+x)
arctan (x)
Geometric Series
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
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
-t
2
term-by-term.
More...
Close
--
DickFurnas
- 16 Nov 2008
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Topic revision: r5 - 2017-10-18
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SteveGaarder
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