In this video, we explore how to **estimate the error in alternating series** using two classic examples: the alternating harmonic series for **ln 2** and the alternating exponential series for **e⁻¹**.
You’ll learn how the **Alternating Series Remainder Theorem** works, how to find how many terms you need for a desired accuracy, and why the **next term** gives you a guaranteed error bound.
We’ll walk step-by-step through both series:
- ln(2) = 1 - 1/2 + 1/3 - 1/4 + ...
- e^(-1) = 1 - 1 + 1/2! - 1/3! + 1/4! - ...
By the end, you’ll understand how alternating signs and decreasing term size make these series converge—and how to tell how close your partial sum is to the true value.
00:00 Introduction
00:35 Understanding the error estimate
02:32 A formula for the error bound
04:03 Example 2 Estimating e^-1
06:36 Wrap Up
