Sum Command

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({"a", "b", "c"}) yields the text "abc".

Sum( <List>, <Number of Elements> )

Calculates the sum of the first n list elements.

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.

Sum({1, 2, 3, 4, 5}, {3, 2, 4, 4, 1}) yields a = 40.

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

CAS Syntax

The following command only works in the Menu view cas.svg 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 \(\frac{3}\{2}\).