Lower limit of summation

Definition

The lower limit of summation is the starting index value in a summation notation, typically represented by the variable at the bottom of the sigma symbol. It indicates where the sum begins.

5 Must Know Facts For Your Next Test

1. The lower limit of summation specifies the initial value for which terms are included in the series.
2. It is usually written below the sigma notation, as part of defining the range of summation.
3. Changing the lower limit affects both the number of terms and their values in a series.
4. In some cases, adjusting both upper and lower limits might keep partial sums unchanged if done correctly.
5. The lower limit can be any integer and is not limited to zero or one.

Review Questions

• What does changing the lower limit of summation do to a series?
• Where is the lower limit located in summation notation?
• How does altering both upper and lower limits simultaneously affect a series?

Related terms

Upper Limit of Summation: The ending index value in a summation notation that indicates where the sum terminates.

Sigma Notation: A compact way to represent a sum using the Greek letter sigma (Σ), specifying both upper and lower limits.

Index Variable: The variable used within sigma notation that takes on each integer value from the lower to upper limits inclusively.