Difference between revisions of "Sum Command"

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:{{example|1=<div>
 
:{{example|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 ''1- r<sup><math>\frac{n+1}{1-r}</math></sup>''.
+
:*<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 14:18, 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] yields 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 \frac{r^{n+1} - 1}{r - 1}.
  • Sum[(1/3)^i, i, 0, Infinity] yields \frac{3}{2}.
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