| Infinite
Sequences and Series
This is
a section that you got a taste of last year, but you will really sink your
teeth into it this year. This section is composed of Limits of Infinite
Sequences, Sums of Infinite Series, Sigma Notation, and Mathematical Induction.
The Limits discussed in the first part have to do with graphical representations
of the sequences. The limit is a number which that sequence approaches.
Think of the limit as the target of the sequence. You will learn
how to estimate this value. You will also learn situations in which
there is no limit and where there are infinite limits. Sums of Infinite
Series is like Arithmetic and Geometric Series and Their Sums, except that
the series is infinite, not finite. You learn about nth partial sums,
sequence of partial sums, convergence, divergence, and a theorem. The
next part is sigma notation. What�s sigma, you ask? It�s a
Greek symbol that is commonly associated with the series or its sum. You
don�t just put the sigma; you put the summands, limits of summation, and
index. You will also learn the properties of finite sums. Last,
but not least comes Mathematical Induction. This is a method of proof
used to show that a statement is true for all positive integers. Basically,
this section is about proofs! I know how much you loved these in the
past. Have fun!
|
