How is called the analogous of an integral for a function with discrete inputs?

Question

• Suppose function $f$ is the function that gives back as output the amount of dollars earned in a year by a given person , say Peter.

So, for example , $f(1) = 20000$ , $f(2) = 30000$ , $f(3) = 25000$ etc.

• How is called a function that would be the analogous of an integral ( or " accumulation function") of $f$ ?

I mean, a function giving back as output the total amount of money earnerd by Peter from year $1$ to year $n$?

This function would map $1$ to $20000$ , $2$ to $(20000+30000)$ , $3$ to $(20000+30000+25000)$, etc.

Answer 1

(Presumably, you refer to the antiderivative or indefinite integral, which is a function.)

The term you are after is the prefix sum. (There is also the suffix sum if you add backwards.)