13.1 导言:序列和系列
章节大纲
-
Patterns exist all around us. One way to model patterns mathematically is with sequences. From how often Halley's Comet is visible, to the height of a bouncing ball, to how much you need to pay for your loan payment—all of these can be modeled by sequences.
::我们周围都存在模式模式。数学模式的一种模式方式是序列。从Halley的彗星的可见频率,到弹跳球的高度,到你需要支付多少贷款——所有这些都可以用序列模型来模拟。We will also discuss series in this chapter. Series can be used to approximate functions, which makes them extremely useful in many applications. We will not cover this specific application in this chapter, but will begin to lay the groundwork to explore it in future math classes.
::我们还将在本章中讨论系列。 系列可以用于大致的功能,这使得这些功能在许多应用中极为有用。 我们不会在本章中涉及这一具体应用,而是将开始奠定基础,在今后的数学课中加以探讨。By the end of this chapter, you should be able to:
::在本章末尾,你应当能够:-
Identify a sequence, particularly an arithmetic sequence and a geometric sequence.
::识别序列,特别是算术序列和几何序列。 -
Find the nth term in a sequence.
::在序列中查找 nth 术语 。 -
Find a formula for a sequence.
::为序列寻找公式。 -
Use summation notation to describe a sum of terms.
::使用总和符号表示术语的总和。 -
Find the sum of a finite arithmetic or geometric se
ries
.
::查找有限算术或几何序列的总和。 -
Find partial sums and the sum of an infinite geometric sequence.
::查找部分和无限几何序列的总和。 -
Identify the coefficients of a binomial expansion using Pascal's Triangle or combinations.
::使用帕斯卡尔三角或组合确定二进制扩张系数。 -
Expand a binomial using the Binomial Theorem.
::使用二进制定理扩展二进制 。
Features
::特征特征-
Section 2: Just a Fluke
::第2节:只是一瞬间 -
Section 4: Giving Credit
::第4节:给予信贷 -
Section 8: Hot Topics
::第8节:热专题
Connections
::连接连接-
The Fibonacci Sequence
::Fibonacci 序列 -
Zeno's Paradoxes
::泽诺的悖论
-
Identify a sequence, particularly an arithmetic sequence and a geometric sequence.