# Difference between revisions of "Sum Command"

##### Command Categories (All commands)

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 a = 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}.
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