 
Summary: Chapter 2
Sequences, Series, and Limits
In this chapter we will introduce the mathematical constructs sequences and series and, in order to deal with
them, we will introduce the first version of one of the central tools of advanced mathematics, the limit. Sequences
are (possibly infinite) ordered lists of numbers. Series are obtained by adding up the numbers in a sequence in
the order in which they appear in the sequence. Limits are a tool for dealing with infinite lists or sums; they
may let us add up an infinite number of numbers or convince us it is impossible, depending on the membership
of the list. We will focus on geometric series which have a number of applications in financial mathematics.
Lending, interest, and related financial instruments are key to making a modern economy work. Interestingly,
loans and interest are very old issues in human civilization. Interest or excessive interest (called usury) is strongly
condemned by Roman Law and many major religions. Even the immortal bard weighed in on the issue through
his character Polonius. The first serious text on financial mathematics was published in 1613 demonstrating that
finance is one of the founding applications of the mathematical sciences. It contained tables that precomputed
compound interest at various rates of interest, a useful tool in a society without out modern access to machine
computation.
Take no usury or interest from
him; but fear your God, that your
brother may live with you. You
shall not lend him your money for
usury, nor lend him your food at
