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== '''[[Geometric sequence]]''' ==
== '''[[Digital rights management]]''' ==
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'''Digital rights management (DRM)''' refers to the laws and technologies which provide intellectual property owners control over the distribution and use of their material by controlling consumers' use of it. The claimed goals are to prevent copying of digital media and to restrict access and content use to what is allowed by [[copyright]] law.<ref name=Bates>Bates, BJ. (2008) 'Commentary: Value and Digital Rights Management-A Social Economics Approach', Journal of Media Economics, 21:1, 53-77</ref>


A '''geometric sequence''' (or '''geometric progression''') is a (finite or infinite) [[sequence]]
Critics refer to it as "Digital ''Restrictions'' Management", and argue that many of the restrictions it enforces go well beyond the rights granted by law.
of (real or complex) numbers
such that the quotient (or ratio) of consecutive elements is the same for every pair.


In finance, compound [[interest rate|interest]] generates a geometric sequence.
==History==
Copyright law is the earliest form of [[intellectual property]] protection.  This area of law developed for print media, long before copying machines and digital media, and has not necessarily kept pace with technology.
=== Legal Background ===
The [[Copyright|copyright]] since its formal creation in 1710 by the British [[Statute of Anne]] and its inclusion in the [[U.S. Constitution]]<ref name=Bennett>Bennett, S. (1999) 'Authors' Rights', Journal of Electronic Publishing, vol. 5, no. 2, Dec., 1999</ref> has been the main protection scheme for intellectual property rights for creative information goods and services.


=== Examples ===
Article I, Section 8, Clause 8 of the [[U.S. Constitution]]:
''"To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries."''


Examples for geometric sequences are
[[Copyright]] law grants exclusive legal ownership of information under specific conditions and terms. Through two major revisions of U.S. copyright law in 1909 and 1976,<ref name=CopyAct1976>{{citation
| title = Copyright Act (17 U.S.C.) Index
| url =  http://www.bitlaw.com/source/17usc/
| first = Daniel A. | last = Tysver }}</ref>
the range of content and media forms covered by legislation were expanded.


* <math> 3, 6, 12, 24, 48, 96            </math> (finite, length 6: 6 elements, quotient 2)
During the pre-digital era, large-scale copying was expensive and usually resulted in degraded content. The development of electronic and digital media transformed the production and distribution of information goods and services. In digital form, the content could be copied perfectly or easily converted to another form or format, and thus lifted the physical constraints of copying.  The rise of digital media and networks made sharing and copying not only easier for traditional information "pirates", but also made it easier for individuals.  Unlike the "pirates" whose unauthorized copies were for commercial gain, individual copying stems from behavioral norms from traditions of [[fair use]] and first-sale rights.


* <math> 1, -2, 4, -8                    </math> (finite, length 4: 4 elements, quotient &minus;2)
''[[Digital rights management|.... (read more)]]''
 
* <math> 8, 4, 2, 1, {1\over2}, {1\over4}, {1\over8},
                    \dots {1\over2^{n-4}}, \dots  </math> (infinite, quotient <math>1\over2</math>)
 
* <math> 2, 2, 2, 2, \dots </math> (infinite, quotient 1)
 
* <math> -2, 2, -2, 2, \dots , (-1)^n\cdot 2 , \dots </math>  (infinite, quotient &minus;1)
 
* <math> {1\over2}, 1, 2, 4, \dots , 2^{n-2}, \dots </math>  (infinite, quotient 2)
 
* <math> 1, 0, 0, 0, \dots \ </math> (infinite, quotient 0) (See [[#General form|General form]] below)
 
=== Application in finance ===
 
The computation of compound interest leads to a geometric series:
 
When an initial amount ''A'' is deposited at an interest rate of ''p'' percent per time period
then the value ''A''<sub>n</sub> of the deposit after ''n'' time-periods is given by
 
:: <math> A_n = A \left( 1 + {p\over100} \right)^n </math>
 
i.e., the values
''A''=''A''<sub>0</sub>, ''A''<sub>1</sub>, ''A''<sub>2</sub>, ''A''<sub>3</sub>, ...
form a geometric sequence with quotient ''q'' = 1+(''p''/100).
 
 
''[[Geometric sequence|.... (read more)]]''


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{| class="wikitable collapsible collapsed" style="width: 90%; float: center; margin: 0.5em 1em 0.8em 0px;"
|-
|-
! style="text-align: center;" | &nbsp;[[Geometric sequence|notes]]
! style="text-align: center;" | &nbsp;[[Digital rights management#References|notes]]
|-
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{{reflist|2}}
{{reflist|2}}
|}
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Revision as of 00:57, 3 August 2012

Digital rights management


Digital rights management (DRM) refers to the laws and technologies which provide intellectual property owners control over the distribution and use of their material by controlling consumers' use of it. The claimed goals are to prevent copying of digital media and to restrict access and content use to what is allowed by copyright law.[1]

Critics refer to it as "Digital Restrictions Management", and argue that many of the restrictions it enforces go well beyond the rights granted by law.

History

Copyright law is the earliest form of intellectual property protection. This area of law developed for print media, long before copying machines and digital media, and has not necessarily kept pace with technology.

Legal Background

The copyright since its formal creation in 1710 by the British Statute of Anne and its inclusion in the U.S. Constitution[2] has been the main protection scheme for intellectual property rights for creative information goods and services.

Article I, Section 8, Clause 8 of the U.S. Constitution: "To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries."

Copyright law grants exclusive legal ownership of information under specific conditions and terms. Through two major revisions of U.S. copyright law in 1909 and 1976,[3] the range of content and media forms covered by legislation were expanded.

During the pre-digital era, large-scale copying was expensive and usually resulted in degraded content. The development of electronic and digital media transformed the production and distribution of information goods and services. In digital form, the content could be copied perfectly or easily converted to another form or format, and thus lifted the physical constraints of copying. The rise of digital media and networks made sharing and copying not only easier for traditional information "pirates", but also made it easier for individuals. Unlike the "pirates" whose unauthorized copies were for commercial gain, individual copying stems from behavioral norms from traditions of fair use and first-sale rights.

.... (read more)