Sum Command

Sum( <List> ): Calculates the sum of all the elements in the list.

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 elements in the list.

Sum({1, 2, 3, 4, 5, 6}, 4) yields the number a = 10.

Sum( <List>, <List of Frequencies> ): Returns the sum of the given list of values, considering the related 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.
Lists must contain objects of the same type.

CAS Syntax

The following command works only in the CAS View.

Sum( <Expression>, <Variable>, <Start Value>, <End Value> ): Computes the sum \(\sum_{t=Start Value}^{End Value}f(t)\). End value can also be infinity.

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 \(\frac{3}{2}\).