Part 1/5:
Understanding the Convergence of Sequences
The study of sequences and their limits is a foundational topic in calculus and analysis. In this article, we'll explore two main exercises related to the convergence of sequences, including the steps to prove convergence and an example that illustrates how to find the limit of a specific recurrence relation.
Part A: Proof of Convergence of a Sequence
To show that if a sequence (a_n) is convergent, then it holds that:
[
\lim_{n \to \infty} a_{n+1} = \lim_{n \to \infty} a_n = L
]