Difference between revisions of "Sum Command"

Revision as of 22:19, 2 August 2019

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 command works for numbers, points, vectors, text, and functions.

CAS Syntax

The following command only works in the CAS View.

Sum( <Expression>, <Variable>, <Start Value>, <End Value> )

Computes sum \sum_{t=Start Value}^{End Value}f(t). End value might be infinity.

Examples:

Sum(n^2, n, 1, 3) yields 14.
Sum(r^k, k, 0, n) yields \frac{r^{n+1} }{r - 1} - \frac{1}{r - 1}.
Sum((1/3)^n, n, 0, Infinity) yields \frac{3}{2}.

@@ Line 1: / Line 1: @@
-<noinclude>{{Manual Page|version=4.2}}</noinclude>
+<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|statistics}}
-{{command|cas=true|statistics}}
+;Sum( <List> )
-;Sum[ <List> ]
 :Calculates the sum of all list elements.
 :{{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, 5)''.
-:* <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.}}
+;Sum( <List>, <Number of Elements> )
-;Sum[ <List>, <Number n of 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>, &lt;List of Frequencies> )
-; Sum[ <List of Numbers>, <List of 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 ''a = 40''.</div>}}
+{{note| 1=This command works for numbers, points, vectors, text, and functions.}}
 ==CAS Syntax==
+The following command only works in the [[File:Menu view cas.svg|link=|16px]] [[CAS View]].
-;Sum[ <List> ]
+;Sum( <Expression>, <Variable>, <Start Value>, <End Value> )
-:Calculates the sum of all list elements.
+:Computes sum <math>\sum_{t=Start Value}^{End Value}f(t)</math>. End value might be infinity.
-:{{examples|1=<div>
-:* <code><nowiki>Sum[{1, 2, 3}]</nowiki></code> yields ''6''.
-:* <code><nowiki>Sum[{a, b, c}]</nowiki></code> yields ''a + b + c''.</div>}}
-;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.
 :{{examples|1=<div>
-:* <code><nowiki>Sum[i^2, i, 1, 3]</nowiki></code>  yields ''14''.
+:* <code><nowiki>Sum(n^2, n, 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^k, k, 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)^n, n, 0, Infinity)</nowiki></code>  yields ''<math>\frac{3}{2}</math>''.</div>}}

Difference between revisions of "Sum Command"

Revision as of 22:19, 2 August 2019

Sum

Command Categories (All commands)

CAS Syntax