sometimes referred to as Euler’s magic formula.
† This is an optional topic not in the BC Course Description. We include it here because of the dramatic result.
Chapter Summary
In this chapter, we have reviewed an important BC Calculus topic, infinite series. We have looked at
a variety of tests to determine whether a series converges or diverges. We have worked with
functions defined as power series, reviewed how to derive Taylor series, and looked at the
Maclaurin series expansions for many commonly used functions. Finally, we have reviewed how to
find bounds on the errors that arise when series are used for approximations.
Practice Exercises
Part A. Directions: Answer these questions without using your calculator.
Note: No questions on sequences will appear on the BC examination. We have nevertheless chosen to
include the topic in Questions 1–5 because a series and its convergence are defined in terms of
sequences. Review of sequences will enhance understanding of series.
- Which sequence converges?
(A)
(B)
(C)
(D)
(E)
2.
(A) sn diverges by oscillation
(B) sn converges to zero
(C)
(D) sn diverges to infinity
(E) None of the above is true.- The sequence
(A) is unbounded
(B) is monotonic
(C) converges to a number less than 1
(D) is bounded