Limits of Sequences

The limit of a sequence is one of the fundamental concepts of calculus. It describes the trend of a sequence as the number of terms tends to infinity. This concept is an important bridge from the discrete to the continuous and from the finite to the infinite.

What Is a Limit?

Consider the sequence: $\frac{1}{1}, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \ldots, \frac{1}{n}, \ldots$

As $n$ grows larger, $\frac{1}{n}$ gets closer and closer to 0. We say: the limit of the sequence $\{\frac{1}{n}\}$ is 0.

Written as: $\lim_{n \to \infty} \frac{1}{n} = 0$