Chapter 11 Summary and Review
Study Guide
Key Terms and Concepts  Examples 

Section 11.1: Sequences and Series 

An infinite sequence is a function having for its domain the set of positive integers $\{1,\text{}2,\text{}3,\text{}4,\text{}5,\dots \}$. A finite sequence is a function having for its domain a set of positive integers $\{1,\text{}2,\text{}3,\text{}4,\text{}5,\dots ,n\}$ for some positive integer n. 
The first four terms of the sequence whose general term is given by ${a}_{n}=3n+2$ are $$\begin{array}{rcl}{a}_{1}\hfill & =\hfill & 3\cdot 1+2=5,\hfill \\ {a}_{2}\hfill & =\hfill & 3\cdot 2+2=8,\hfill \\ {a}_{3}\hfill & =\hfill & 3\cdot 3+2=11,\text{\hspace{1em}}\text{and}\hfill \\ {a}_{4}\hfill & =\hfill & 3\cdot 4+2=14.\hfill \end{array}$$ 
The sum of the terms of an infinite sequence is an infinite series. A partial sum is the sum of the first n terms. It is also called a finite series or the nth partial sum and is denoted ${S}_{n}$. 
For the sequence above, ${S}_{4}=5+8+11+14$, or 38. We can denote this sum using ... 
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