Upper limit of summation

Definition

The upper limit of summation is the highest value that the index variable reaches in a summation notation. It determines the end point of the sum.

5 Must Know Facts For Your Next Test

1. In the notation $\sum_{i=1}^{n} a_i$, 'n' is the upper limit of summation.
2. The upper limit can be any integer, including negative values.
3. The value of the upper limit dictates how many terms are included in the sum.
4. Adjusting the upper limit changes the overall value of the summation.
5. In infinite series, the upper limit is often represented by infinity (∞).

Review Questions

• What does changing the upper limit of summation affect in a series?
• In $\sum_{k=1}^{5} k^2$, what is the upper limit of summation?
• How would you represent an infinite series using summation notation?

Related terms

Lower Limit of Summation: The lowest value that the index variable takes in a summation.

Index Variable: The variable that represents each term's position in a sequence or series.

Infinite Series: A series that continues indefinitely without terminating.