Part 1/5:

Understanding Limits in Mathematics

Limits are a fundamental concept in mathematics, often serving as the backbone of calculus. They help us understand how functions behave as they approach particular points or infinity. In this discussion, we will explore the nature of limits through sequences and graphical interpretations.

The Concept of Limits with Sequences

Consider a simple sequence of numbers: 1, 1/2, 1/3, 1/4, 1/5, and so forth. As this sequence progresses, you can observe that the values get closer and closer to zero. Notably, if you continue this pattern indefinitely, you can see that as n approaches infinity, the term ( 1/n ) will converge to zero. This concept can be encapsulated using the limit notation:

[

\lim_{n \to \infty} \frac{1}{n} = 0

]