Series (BC)

Quick Notes

• Sequences and series are a BIG topic on the BC exam, and it is always both on the MCQ as well as #6 on the FRQ.

• You may need to determine (and justify) whether or not a sequence or series converges or diverges.

• When using any convergence test, be sure to STATE THE CONDITIONS!

• For Geometric Series, you may be asked for the value of convergence.

• Harmonic and Alternating Harmonic series show up quite frequently.

• You may be asked to determine whether a series converges conditionally or absolutely.

• You will likely be asked to write the Taylor or Maclaurin (centered at x = 0) polynomial to a certain degree. You might also be asked to write the general term for the series or find a specific coefficient.

• Remember that Taylor Polynomials are used to APPROXIMATE a function (they are not equal), and a Taylor Series is equal to the function on the interval of convergence.

• You will likely be asked to determine the radius and/or interval of convergence of a series. These are the x-values for which the series converges. This can usually be done using the ratio test, but be sure to check the endpoints when determining the interval.

• You should know the Maclaurin Series for e^x, sin x, and cos x, and you should be able to recognize rational functions that can be represented as a geometric series.

• Be prepared to manipulate series through substitution, differentiation, and integration.

• If asked to approximate the value of a function, you will likely also be asked to bound the error. Use either Lagrange Error Bound or Alternating Series Error Bound.

~ Related CED Units ~ 10

FRQ Samples

2024 BC 6

2023 BC 6

2022 BC 6

2021 BC 6

2019 BC 6

2017 BC 6

2016 BC 6

2011 BC 6

2004 BC 6

~ Reference Sheet ~

Convergence Tests