Difference between revisions of "Sum Command"

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;Sum[ <List> ]
 
;Sum[ <List> ]
 
:Calculates the sum of all list elements.
 
:Calculates the sum of all list elements.
:{{example|1=<div>
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:{{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>''.
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;Sum[ <List> ]
 
;Sum[ <List> ]
 
:Calculates the sum of all list elements.
 
:Calculates the sum of all list elements.
:{{example|1=<div>
+
:{{examples|1=<div>
 
:* <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>}}
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;Sum[ <Expression f(t)>, <Variable t>, <Start Value s>, <End Value e>]
 
;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=<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} - 1}{r - 1}</math>''.

Revision as of 19:27, 19 December 2012


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, 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] yields the number a = 10.
Note: This command works 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 f(t)>, <Variable t>, <Start Value s>, <End Value e>]
Computes sum \sum_{t=s}^{e}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} - 1}{r - 1}.
  • Sum[(1/3)^i, i, 0, Infinity] yields \frac{3}{2}.


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