Calculus How To

Continued Sum: Definition and Examples

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What is “Continued Sum”?

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

1. Sigma Notation

continued sumIn 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:
X1 + X2 + …Xn

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.


Calculus Notation. Retrieved October 12, 2019 from:

Stephanie Glen. "Continued Sum: Definition and Examples" From Calculus for the rest of us!

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