Alternating Series Error Bound

#10.10 Alternating Series Error Bound

Welcome to AP Calc 10.10! In this lesson, you’ll learn how to estimate the accuracy of a partial sum for an alternating series.

#➕ Alternating Series Error Bound Theorem

The error bound theorem for an alternating series states that for a convergent alternating series, $\sum^\infty_{n=1}(-1)^n\cdot a_n$, we can estimate its true value by using an error bound. The error bound is defined as $a_i$. We can estimate the true value of the sum ($s$) with the following equation: $|s-s_{i-1}|\leq a_i$ where $i$ is the first omitted term of our estimation.

That’s a lot of information—now let’s break it down with an example!

#🧱 Breaking Down the Theorem

The first thing we need is a convergent, alternating series. Let’s use this one:

\sum_{n=1}^\inf...