# TI-BASIC:Cumsum

**Command Summary**

Calculates cumulative sums of a list or of the columns of a matrix.

**Command Syntax**

cumSum(*list or matrix*)

**Menu Location**

Press:

- 2nd LIST to access the list menu.
- RIGHT to access the OPS submenu.
- 6 to select cumSum(, or use arrows.

Alternatively, press:

- MATRX (TI-83) or 2nd MATRX (TI-83+ or higher) to access the matrix menu.
- RIGHT to access the MATH submenu.
- 0 to select cumSum(, or use arrows.

TI-83/84/+/SE

2 bytes

cumSum( calculates the cumulative sums of a list, or of the columns of a matrix, and outputs them in a new list or matrix variable.

For a list, this means that the Nth element of the result is the sum of the first N elements of the list:

cumSum({1,3,5,7,9}) {1 4 9 16 25}

For a matrix, cumSum( is applied to each column in the same way as it would be for a list (but numbers in different columns are never added):

[[0,1,1][0,1,3][0,1,5][0,1,7]] [[0 1 1] [0 1 3] [0 1 5] [0 1 7]] cumSum(Ans) [[0 1 1] [0 2 4] [0 3 9] [0 4 16]]

# Advanced Uses

The ΔList( command is very nearly the inverse of the cumSum( command - it calculates the differences between consecutive elements. For any list, ΔList(cumSum(*list*)) will return the same list, but without its first element:

ΔList(cumSum({1,2,3,4,5,6,7})) {2 3 4 5 6 7}

Removing the first element would otherwise be a difficult procedure involving the seq( command, so this is a useful trick to know.

For a matrix, if you want to sum up the rows instead of the columns, use the ^{T} (Transpose) command.