The following figures show what is meant by the Limit of a Sequence. Scroll down the page for more examples and solutions.

The Limit of a Sequence
The concept of determining if sequence converges or diverges.
Example:
Consider the following graphs of sequences.
Do they appear to have a limit?
a
n = {1 + 1/n}
a
n = {2(-1)
n/n}
Determine if the sequence converges or diverges.
a
n = (3n - 2)/(n - 1)
a
n = -2 + (-1)
n
a
n = ln(n)/5n
a
n = 1/(-2)
n
Finding the Limit of a Sequence
Example:
Find the limit of each given sequence
a) {1/n
3}
b) {(n
2 + 2n + 4)/(3
2 + 1)}
c) {n
3e
-n}
The Squeeze Theorem and Absolute Value Theorem
How to find the limits of some sequences by using the squeeze and / or absolute value theorems?
Example:
Find the limit of the sequence
{1/n
3 sin(n
2)}
Example:
Find the limit of the sequence
x
n = {((-1)
n + n
2)/n
2}
Example:
Find the limit of the sequence
{n
-n3
Try out our new and fun Fraction Concoction Game.
Add and subtract fractions to make exciting fraction concoctions following a recipe.
There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics
of fraction addition and subtraction or challenge yourself with the insane level.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.