Difference between revisions of "Sum Command"
From GeoGebra Manual
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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''. | + | :* <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)''. | + | :* <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)''. | + | :* <code><nowiki>Sum[ {(1, 2), 3} ]</nowiki></code> yields the point ''B = (4, 2)''. |
| − | :* <code><nowiki>Sum[{"a", "b", "c"}]</nowiki></code> yields the text ''"abc"''.</div>}} | + | :* <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.}} | :{{note| 1=This command works for numbers, points, vectors, text, and functions.}} | ||
| − | ;Sum[ <List>, <Number | + | ;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=<code>Sum[{1, 2, 3, 4, 5, 6}, 4]</code> yields the number ''a = 10''.}} | ||
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| − | ; Sum[ <List | + | ;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 ''40''.</div>}} | : {{example|1=<div><code><nowiki>Sum[{1, 2, 3, 4, 5},{3, 2, 4, 4, 1}]</nowiki></code> yields ''40''.</div>}} | ||
| Line 33: | Line 33: | ||
:* <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 | + | ;Sum[ <Expression>, <Variable>, <Start Value>, <End Value> ] |
| − | :Computes sum <math>\sum_{t= | + | :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} - 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 10:51, 18 July 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, 2).Sum[ {"a", "b", "c"} ]yields the text "abc".
- Note: This command works for numbers, points, vectors, text, and functions.
- 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.
- Note: This command works for numbers, points, vectors, text, and functions.
- 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 40.
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} - 1}{r - 1}.Sum[(1/3)^i, i, 0, Infinity]yields \frac{3}{2}.
