Loading [MathJax]/jax/output/SVG/config.js
Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Mathematics LibreTexts

Search

  • Filter Results
  • Location
  • Classification
    • Article type
    • Stage
    • Author
    • Cover Page
    • License
    • Show Page TOC
    • Transcluded
    • PrintOptions
    • OER program or Publisher
    • Autonumber Section Headings
    • License Version
    • Print CSS
    • Screen CSS
    • Number of Print Columns
  • Include attachments
Searching in
About 1 results
  • https://math.libretexts.org/Bookshelves/Analysis/Introduction_to_Mathematical_Analysis_I_(Lafferriere_Lafferriere_and_Nguyen)/02%3A_Sequences/2.03%3A_Monotone_Sequences
    Now, we also have \(a_{n} \leq a\) and \(b \leq b_{n}\) for all \(n \in \mathbb{N}\) (since \(\left\{a_{n}\right\}\) is increasing and \(\left\{b_{n}\right\}\) is decreasing). Then \(b=\lim _{n \right...Now, we also have \(a_{n} \leq a\) and \(b \leq b_{n}\) for all \(n \in \mathbb{N}\) (since \(\left\{a_{n}\right\}\) is increasing and \(\left\{b_{n}\right\}\) is decreasing). Then \(b=\lim _{n \rightarrow \infty} b_{n}=\lim _{n \rightarrow \infty}\left[\left(b_{n}-a_{n}\right)+a_{n}\right]=a\). \[\lim _{n \rightarrow \infty} a_{n}=\infty, \lim _{n \rightarrow \infty} b_{n}=\infty, \text { and } \lim _{n \rightarrow \infty} c_{n}=-\infty\]

Support Center

How can we help?