General Contents
Detailed Contents
Index
Programmed tutorial: Sequence and its Limit
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If you want to see all of the following steps at once, click the "All Steps" button. Otherwise, use the "Next" button.
We wish to determine the convergence or divergence of the sequence given by
.
General Contents
Detailed Contents
Index
First, plot the terms of this series on paper.
Then check your graph by clicking on “Next”.
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Does it
look
like the sequence is converging?
Yes.
What appears to be the approximate limit?
The limit appears to be approximately -0.35.
How can we check convergence analytically?
We can try finding the limit of
Set that up.
Simplify by dividing numerator and denominator by
n
.
What is the limit of the
Use this result to evaluate the limit,
L
.
What can we conclude here?
The sequence
converges to
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.