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Alternating Series Error Bound

Definition

The alternating series error bound provides an upper bound on the absolute error when approximating an alternating series using only a finite number of terms. It helps determine how close our partial sum is to the actual value of the series.

Analogy

Imagine you are trying to estimate how much money you will have after depositing money into a bank account that gives alternating interest rates. The alternating series error bound acts like a guarantee that tells you how much your estimated balance can differ from your actual balance. If your estimated balance falls within this range, you know your approximation using a finite number of terms is accurate enough.

Related terms

Alternating Series: An alternating series is a series where each term alternates in sign (positive and negative).

Convergence Test: A convergence test helps determine whether an infinite series converges or diverges based on certain criteria.

Partial Sum: A partial sum is the sum of only a finite number of terms in an infinite series. It represents an approximation to the total sum but may not be exact.