AP Calc BC Lesson 10.10 is all about estimating the true value of a convergent infinite alternating series. We will do this by finding a partial sum and then finding an error bound. Basically, we will find a range in which the sum of the true infinite series lies based on an estimate (partial sum). Let’s see how we can do this!
Alternating Series Error Bound
For a convergent alternating series with infinite sum S and partial sum 
,
In other words, the error is less than or equal to the next unused term. Let’s try some examples to see how this works! Feel free to try your hand at the problem before viewing the solution.
Examples
Solutions
Key Concepts
- The alternating series must converge to use an alternating series error bound.
- The alternating series error bound is obtained by plugging in the (n+1) value to the absolute value of the original series.
