Technical Mathematics, Sixth Edition

Chapter 20. Sequences, Series, and the Binomial Theorem

OBJECTIVES When you have completed this chapter, you should be able to Identify various types of sequences and series. Write the general term or a recursion relation for many series. Compute any term or the sum of any number of terms of an arithmetic progression or a geometric progression. Compute any term of a harmonic progression. Insert any number of arithmetic means, harmonic means, or geometric means between two given numbers. Compute the sum of an infinite geometric progression. Compute, graph, and find sums of sequences by calculator. Solve applications problems using series. Raise a binomial to a power using the binomial theorem. Find any term in a binomial expansion.

We start this chapter with a general introduction to sequences and series. Sequences and series are of great interest because a computer or calculator uses series internally to calculate many functions, such as the sine of an angle, the logarithm of a number, and so on. We then cover some specific sequences, such as the arithmetic progression and the geometric progression. Progressions are used to describe such things as the sequence of heights reached by a swinging pendulum on subsequent swings or the monthly balance on a savings account that is growing with compound interest.

We finish this chapter with an introduction to the binomial theorem. The binomial theorem enables us to expand a binomial, such as (3x² − 2y)⁵, without actually having to multiply the ...