## What is “Continued Sum”?

**Continued sum** is an informal term that can mean one of several things in mathematics.

## 1. Sigma Notation

In calculus, continued sum usually refers to Sigma (summation) notation. Summation notation involves adding up every point in a set of data—a continuation of summing, or summing up over and over again.

## 2. Integration

Continued sum might also refer to integration and the integral sign ( ∫ ). That’s because integration involves —like it’s cousin, sigma notation — adding up again and again. The difference between sigma notation though, is that with integrals you’re adding up infinitely many tiny pieces; summation notation usually involves finite (fixed) amounts, or at least, very well defined amounts.

Leibniz popularized a “∫” as notation of the continued sum to find the area under a curve.

## 3. A…Continued Sum

Sometimes the term might just refer to something a little simpler than integration or sigma. It might mean “a sum that goes on—and on.”

For example:

X_{1} + X_{2} + …X_{n}

Usually, in calculus, these are called “series” or “infinite series” (if the series goes on until infinity). Outside of calculus (for example, in elementary algebra), you might see them called continued sums.

## References

Calculus Notation. Retrieved October 12, 2019 from: https://ssp2017cub.files.wordpress.com

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