Difference between revisions of "Sum Command"

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:Calculates the sum of all list elements.
 
:Calculates the sum of all list elements.
 
:{{examples|1=<div>
 
:{{examples|1=<div>
:* <code><nowiki>Sum[ {1, 2, 3}]</nowiki></code> yields the number ''a = 6''.
+
:* <code><nowiki>Sum[{1, 2, 3}]</nowiki></code> yields the number ''a = 6''.
:* <code><nowiki>Sum[ {x^2,  x^3} ]</nowiki></code> yields ''f(x) = x<sup>2</sup> + x<sup>3</sup>''.
+
:* <code><nowiki>Sum[{x^2,  x^3}]</nowiki></code> yields ''f(x) = x<sup>2</sup> + x<sup>3</sup>''.
:* <code><nowiki>Sum[ Sequence[ i, i, 1, 100 ] ]</nowiki></code> yields the number ''a = 5050''.
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:* <code><nowiki>Sum[Sequence[ i, i, 1, 100 ]]</nowiki></code> yields the number ''a = 5050''.
:* <code><nowiki>Sum[ {(1, 2), (2, 3)} ]</nowiki></code> yields the point ''A = (3, 5)''.
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:* <code><nowiki>Sum[{(1, 2), (2, 3)}]</nowiki></code> yields the point ''A = (3, 5)''.
:* <code><nowiki>Sum[ {(1, 2), 3} ]</nowiki></code> yields the point ''B = (4, 2)''.
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:* <code><nowiki>Sum[{(1, 2), 3}]</nowiki></code> yields the point ''B = (4, 5)''.
:* <code><nowiki>Sum[ {"a", "b", "c"} ]</nowiki></code> yields the text ''"abc"''.</div>}}
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:* <code><nowiki>Sum[{"a", "b", "c"}]</nowiki></code> yields the text ''"abc"''.</div>}}
:{{note| 1=This command works for numbers, points, vectors, text, and functions.}}
 
 
 
 
 
 
;Sum[ <List>, <Number of Elements> ]
 
;Sum[ <List>, <Number of Elements> ]
 
:Calculates the sum of the first ''n'' list elements.  
 
:Calculates the sum of the first ''n'' list elements.  
:{{example| 1=<code>Sum[{1, 2, 3, 4, 5, 6}, 4]</code> yields the number ''a = 10''.}}
+
:{{example| 1=<div><code>Sum[{1, 2, 3, 4, 5, 6}, 4]</code> yields the number ''a = 10''.</div>}}
:{{note| This command works for numbers, points, vectors, text, and functions.}}
 
 
 
 
 
 
;Sum[ <List>, <List of Frequencies> ]
 
;Sum[ <List>, <List of Frequencies> ]
 
:Returns the sum of given list of numbers considering the frequencies.
 
:Returns the sum of given list of numbers considering the frequencies.
: {{example|1=<div><code><nowiki>Sum[{1, 2, 3, 4, 5},{3, 2, 4, 4, 1}]</nowiki></code> yields ''a = 40''.</div>}}
+
:{{example|1=<div><code><nowiki>Sum[{1, 2, 3, 4, 5}, {3, 2, 4, 4, 1}]</nowiki></code> yields ''a = 40''.</div>}}
 
+
{{note| 1=This commands work for numbers, points, vectors, text, and functions.}}
 
 
 
 
 
==CAS Syntax==
 
==CAS Syntax==
 
 
;Sum[ <List> ]
 
;Sum[ <List> ]
 
:Calculates the sum of all list elements.
 
:Calculates the sum of all list elements.
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:* <code><nowiki>Sum[{1, 2, 3}]</nowiki></code> yields ''6''.
 
:* <code><nowiki>Sum[{1, 2, 3}]</nowiki></code> yields ''6''.
 
:* <code><nowiki>Sum[{a, b, c}]</nowiki></code> yields ''a + b + c''.</div>}}
 
:* <code><nowiki>Sum[{a, b, c}]</nowiki></code> yields ''a + b + c''.</div>}}
 
 
;Sum[ <Expression>, <Variable>, <Start Value>, <End Value> ]
 
;Sum[ <Expression>, <Variable>, <Start Value>, <End Value> ]
 
:Computes sum <math>\sum_{t=Start Value}^{End Value}f(t)</math>. End value might be infinity.
 
:Computes sum <math>\sum_{t=Start Value}^{End Value}f(t)</math>. End value might be infinity.
 
:{{examples|1=<div>
 
:{{examples|1=<div>
 
:* <code><nowiki>Sum[i^2, i, 1, 3]</nowiki></code>  yields ''14''.
 
:* <code><nowiki>Sum[i^2, i, 1, 3]</nowiki></code>  yields ''14''.
:* <code><nowiki>Sum[r^i, i, 0, n]</nowiki></code>  yields ''<math>\frac{r^{n+1} - 1}{r - 1}</math>''.
+
:* <code><nowiki>Sum[r^i, i, 0, n]</nowiki></code>  yields ''<math>\frac{r^{n+1} }{r - 1} - \frac{1}{r - 1}</math>''.
 
:* <code><nowiki>Sum[(1/3)^i, i, 0, Infinity]</nowiki></code>  yields ''<math>\frac{3}{2}</math>''.</div>}}
 
:* <code><nowiki>Sum[(1/3)^i, i, 0, Infinity]</nowiki></code>  yields ''<math>\frac{3}{2}</math>''.</div>}}

Revision as of 13:07, 5 September 2013



Sum[ <List> ]
Calculates the sum of all list elements.
Examples:
  • 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, 5).
  • Sum[{"a", "b", "c"}] yields the text "abc".
Sum[ <List>, <Number of Elements> ]
Calculates the sum of the first n list elements.
Example:
Sum[{1, 2, 3, 4, 5, 6}, 4] yields the number a = 10.
Sum[ <List>, <List of Frequencies> ]
Returns the sum of given list of numbers considering the frequencies.
Example:
Sum[{1, 2, 3, 4, 5}, {3, 2, 4, 4, 1}] yields a = 40.
Note: This commands work for numbers, points, vectors, text, and functions.

CAS Syntax

Sum[ <List> ]
Calculates the sum of all list elements.
Examples:
  • Sum[{1, 2, 3}] yields 6.
  • Sum[{a, b, c}] yields a + b + c.
Sum[ <Expression>, <Variable>, <Start Value>, <End Value> ]
Computes sum \sum_{t=Start Value}^{End Value}f(t). End value might be infinity.
Examples:
  • Sum[i^2, i, 1, 3] yields 14.
  • Sum[r^i, i, 0, n] yields \frac{r^{n+1} }{r - 1} - \frac{1}{r - 1}.
  • Sum[(1/3)^i, i, 0, Infinity] yields \frac{3}{2}.
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