# Famous Series

## Geometric Series

## P-Series

## Harmonic Series

- 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.

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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 *-t*^{2} term-by-term.

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-- DickFurnas - 16 Nov 2008

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Topic revision: r5 - 2017-10-18 - SteveGaarder