Index

Definition

An index is a numerical or symbolic label used to specify elements within a sequence or sum. In calculus, indices often denote the terms in a sum representing an approximation.

5 Must Know Facts For Your Next Test

1. Indices are commonly used in Riemann sums to represent individual subintervals.
2. The index \( i \) often ranges from 1 to \( n \), where \( n \) is the number of subintervals.
3. Changing the value of the index shifts which term in the sequence is being referred to.
4. In summation notation, the index appears below and above the summation symbol (∑).
5. Indices can be manipulated algebraically when simplifying expressions involving sums.

Review Questions

• What role does an index play in a Riemann sum?
• How does changing the value of an index affect a summation?
• Where do you typically see indices appear in mathematical notation for approximating areas?

Related terms

Riemann Sum: A method for approximating the total area underneath a curve by dividing it into simple shapes whose areas can be calculated.

Subinterval: A smaller interval within a larger interval, used in methods like Riemann sums to approximate integrals.

$\Sigma$ Notation: $\Sigma$ notation is another way of writing sums with multiple terms using an index to indicate each term's position.