Monotonic Sequences and their Limits

Abstract

This article explores the concept of monotonic sequences, which are sequences that either consistently increase or decrease. It delves into the definitions of monotonically increasing and decreasing sequences, and discusses key properties such as boundedness and convergence. The article highlights the Monotone Convergence Theorem, which states that every bounded monotonic sequence converges to a limit. Examples of monotonic sequences are provided to illustrate these concepts. Additionally, the article examines the applications of monotonic sequences in calculus, numerical analysis, and optimization, emphasizing their importance in both theoretical and practical contexts