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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.

Limit of a Sequence

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?
an = {1 + 1/n}
an = {2(-1)n/n}
Determine if the sequence converges or diverges.
an = (3n - 2)/(n - 1)
an = -2 + (-1)n
an = ln(n)/5n
an = 1/(-2)n
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}



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)} Example:
Find the limit of the sequence
xn = {((-1)n + n2)/n2} Example:
Find the limit of the sequence
{n-n3

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