Limit of a Sequence

 
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

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Finding the Limit of a Sequence
Example:
Find the limit of each given sequence
a) {1/n³}
b) {(n² + 2n + 4)/(3² + 1)}
c) {n³e^-n}

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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/n³ sin(n²)}

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Example:
Find the limit of the sequence
x_n = {((-1)ⁿ + n²)/n²}

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Example:
Find the limit of the sequence
{n^-n3

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