Index

Definition

An index is a variable used to denote the position of an element within a sequence or array, often used in summation notation. In integration, indices help identify terms in approximations like Riemann sums.

5 Must Know Facts For Your Next Test

1. Indices are commonly denoted by letters such as i, j, or k.
2. In Riemann sums, the index i indicates the subinterval being considered.
3. The upper and lower bounds of summation are defined using indices.
4. Changing the index in a summation does not affect the sum's value.
5. Indices help simplify notation for series and sequences in integral approximations.

Review Questions

• What role does the index play in a Riemann sum?
• How does changing an index affect a summation?
• Why are indices important for defining the bounds of summation?

Related terms

Summation Notation: A mathematical notation used to represent the sum of a sequence of terms, typically expressed with sigma (\( \Sigma \)) and involving an index.

Riemann Sum:

An approximation of an integral by dividing an interval into subintervals and summing up areas of rectangles formed under the curve.

Integral:

\( \int f(x) \, dx \), representing the area under a curve over an interval, calculated as a limit of Riemann sums.