# 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, 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 \mathrm{\mathsf{ \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 \mathrm{\mathsf{ \frac{r^{n+1} }{r - 1} - \frac{1}{r - 1} }}.
• Sum((1/3)^n, n, 0, Infinity) yields \mathrm{\mathsf{ \frac{3}{2} }}.
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