Upper limit of summation

Definition

The upper limit of summation is the highest integer value in the range over which a summation is performed. It indicates where the addition of terms stops in a series.

5 Must Know Facts For Your Next Test

1. The upper limit of summation is represented as the number above the sigma notation ($\sum$).
2. In a finite series, it determines how many terms are included in the sum.
3. The upper limit can be a constant or an algebraic expression.
4. Changing the upper limit changes the total sum of the series.
5. In infinite series, there is no fixed upper limit; instead, it approaches infinity.

Review Questions

• What does the upper limit of summation indicate in a series?
• How would you write out a series with an upper limit of 5 using sigma notation?
• What happens to the total sum if you increase the upper limit by 1?

Related terms

Lower Limit of Summation: The smallest integer value in the range over which a summation is performed. It indicates where the addition of terms begins.

Sigma Notation: A concise way to represent the sum of a sequence using the Greek letter sigma ($\sum$) and indices that denote limits of summation.

Infinite Series: A series that continues indefinitely without terminating, often represented with an infinity symbol as its upper limit.