Difference between revisions of "Sum Command"

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<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
 
<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
 
{{command|statistics}}
 
{{command|statistics}}
; Sum[List]: Calculates the sum of all list elements.
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;Sum[ <List> ]: Calculates the sum of all list elements.
: {{Note| This command works for numbers, points, vectors, text, and functions.}}
+
:{{example|1=<div>
: {{Example|1=&nbsp;
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:* <code><nowiki>Sum[{1, 2, 3}]</nowiki></code> yields the number ''a = 6''.
:* <code>Sum[{1, 2, 3}]</code> gives you the number ''a = 6''.
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:* <code><nowiki>Sum[{x^2, x^3}]</nowiki></code> yields ''f(x) = x<sup>2</sup> + x<sup>3</sup>''.
:* <code>Sum[{x^2, x^3}]</code> gives you ''f(x) = x<sup>2</sup> + x<sup>3</sup>''.
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:* <code><nowiki>Sum[Sequence[i, i, 1, 100]]</nowiki></code> yields the number ''a = 5050''.
:* <code>Sum[Sequence[i,i,1,100]]</code> gives you the number ''a = 5050''.
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:* <code><nowiki>Sum[{(1, 2), (2, 3)}]</nowiki></code> yields the point ''A = (3, 5)''.
:* <code>Sum[{(1, 2), (2, 3)}]</code> gives you the point ''A = (3, 5)''.
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:* <code><nowiki>Sum[{(1, 2), 3}]</nowiki></code> yields the point ''B = (4, 2)''.
:* <code>Sum[{(1, 2), 3}]</code> gives you the point ''B = (4, 2)''.
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:* <code><nowiki>Sum[{"a", "b", "c"}]</nowiki></code> yields the text ''"abc"''.</div>}}
:* <code>Sum[{"a","b","c"}]</code> gives you the text ''"abc"''.}}
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:{{note| 1=This command works for numbers, points, vectors, text, and functions.}}
 
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;Sum[ <List>, <Number n of Elements> ]
; Sum[List, Number n of Elements]: Calculates the sum of the first ''n'' list elements.  
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:Calculates the sum of the first ''n'' list elements.  
: {{Note| This command works for numbers, points, vectors, text, and functions.}}
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:{{example| 1=<code>Sum[{1, 2, 3, 4, 5, 6}, 4]</code> gives you the number ''a = 10''.}}
: {{Example| 1=<code>Sum[{1, 2, 3, 4, 5, 6}, 4]</code> gives you the number ''a = 10''.}}
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:{{note| This command works for numbers, points, vectors, text, and functions.}}
 
 
 
==CAS Syntax==
 
==CAS Syntax==
 
Following syntax works only in CAS view
 
Following syntax works only in CAS view
;Sum[<Expression f(t)>,<Variable t>,<Start Value s>,<End Value e>]
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;Sum[ <Expression f(t)>,<Variable t>,<Start Value s>,<End Value e>]
 
:Computes sum <math>\sum_{t=s}^{e}f(t)</math>. End value might be infinity.
 
:Computes sum <math>\sum_{t=s}^{e}f(t)</math>. End value might be infinity.
:{{Example|1=&nbsp;
+
:{{example|1=<div>
:*<code><nowiki>Sum[i^2, i, 1, 3]</nowiki></code>  returns ''14''.
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:*<code><nowiki>Sum[i^2, i, 1, 3]</nowiki></code>  yields ''14''.
:*<code><nowiki>Sum[r^i, i,0,n]</nowiki></code>  returns ''1- r<sup><math>\frac{n+1}{1-r}</math></sup>''.
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:*<code><nowiki>Sum[r^i, i,0,n]</nowiki></code>  yields ''1- r<sup><math>\frac{n+1}{1-r}</math></sup>''.
:*<code><nowiki>Sum[(1/3)^i, i,0,Infinity]</nowiki></code>  returns ''<math>\frac{3}{2}</math>''.}}
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:*<code><nowiki>Sum[(1/3)^i, i,0,Infinity]</nowiki></code>  yields ''<math>\frac{3}{2}</math>''.</div>}}

Revision as of 13:21, 25 August 2011


Sum[ <List> ]
Calculates the sum of all list elements.
Example:
  • Sum[{1, 2, 3}] yields the number a = 6.
  • Sum[{x^2, x^3}] yields f(x) = x2 + x3.
  • Sum[Sequence[i, i, 1, 100]] yields the number a = 5050.
  • Sum[{(1, 2), (2, 3)}] yields the point A = (3, 5).
  • Sum[{(1, 2), 3}] yields the point B = (4, 2).
  • Sum[{"a", "b", "c"}] yields the text "abc".
Note: This command works for numbers, points, vectors, text, and functions.
Sum[ <List>, <Number n of Elements> ]
Calculates the sum of the first n list elements.
Example: Sum[{1, 2, 3, 4, 5, 6}, 4] gives you the number a = 10.
Note: This command works for numbers, points, vectors, text, and functions.

CAS Syntax

Following syntax works only in CAS view

Sum[ <Expression f(t)>,<Variable t>,<Start Value s>,<End Value e>]
Computes sum \sum_{t=s}^{e}f(t). End value might be infinity.
Example:
  • Sum[i^2, i, 1, 3] yields 14.
  • Sum[r^i, i,0,n] yields 1- r\frac{n+1}{1-r}.
  • Sum[(1/3)^i, i,0,Infinity] yields \frac{3}{2}.
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