Skip to main content\(\newcommand{\N}{\mathbb N}
\newcommand{\Z}{\mathbb Z}
\newcommand{\Q}{\mathbb Q}
\newcommand{\R}{\mathbb R}
\newcommand{\unknown}{{\color{gray} ?}}
\DeclareMathOperator{\arcsec}{arcsec}
\DeclareMathOperator{\arccot}{arccot}
\DeclareMathOperator{\arccsc}{arccsc}
\newcommand{\tuple}[1]{\left\langle#1\right\rangle}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Chapter 8 Sequences and Series (SQ)
Learning Outcomes
By the end of this chapter, you should be able to...
Define and use explicit and recursive formulas for sequences.
Determine if a sequence is convergent, divergent, monotonic, or bounded, and compute limits of convergent sequences.
Compute the first few terms of a telescoping or geometric partial sum sequence, and find a closed form for this sequence, and compute its limit.
Determine if a geometric series converges, and if so, the value it converges to.
Use the divergence, alternating series, and integral tests to determine if a series converges or diverges.
Use the direct comparison and limit comparison tests to determine if a series converges or diverges.
Use the ratio and root tests to determine if a series converges or diverges.
Determine if a series converges absolutely or conditionally.
Readiness Assurance.
Before beginning this chapter, you should be able to...
-
Compute limits.
-
Express the sum of indexed values using summation notation.
-
Evaluate indefinite integrals.
