Glossary
Accuracy of Estimation
A measure of how close a partial sum approximation is to the true value of a convergent alternating series, directly related to the magnitude of the error bound.
Example:
A smaller error bound indicates a higher accuracy of estimation, meaning your approximation is very close to the actual sum.
Alternating Series Error Bound
A theorem used for a convergent alternating series to estimate the accuracy of a partial sum approximation of its true value.
Example:
When approximating the sum of an alternating series, the Alternating Series Error Bound tells you how close your approximation is to the true sum.
Convergent Alternating Series
An alternating series that satisfies the conditions of the Alternating Series Test, meaning its terms decrease in absolute value and approach zero, causing the series to sum to a finite value.
Example:
The series is a convergent alternating series because it satisfies the conditions of the Alternating Series Test.
Error Bound
For a convergent alternating series, this is the maximum possible difference between the true sum of the series and a partial sum approximation, defined by the absolute value of the first omitted term.
Example:
If your approximation of a series has an error bound of 0.01, it means your true answer is within 0.01 of your approximation.
First Omitted Term
In the context of the Alternating Series Error Bound, this is the absolute value of the first term of the series that is not included in the partial sum approximation, and it determines the error bound.
Example:
If you use the first 5 terms to estimate a series, the 6th term, , represents the first omitted term and determines your error bound.
Partial Sum
The sum of a finite number of terms of an infinite series, used as an approximation for the true sum of the entire series.
Example:
If you add up the first 10 terms of a series, you've calculated a partial sum that approximates the infinite sum.