General Contents
Detailed Contents
Index
Programmed tutorial: Root Test of Convergence or Divergence of a Series: Example 1
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Use the Root Test to determine the convergence or divergence of the series
General Contents
Detailed Contents
Index
First, plot the terms of this series on paper.
To check, click “Next”.
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To get further insight, plot the sequence of partial sums on paper.
Then check by clicking “Next”.
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Does it appear that the series is converging?
Yes, the partial sums appear to be approaching approximately 1.8.
State the Root Test.
We test
What is the condition on this limit that indicates convergence?
We must have
What is the form of
a
n
for this series?
Find the nth root of |
a
n
|.
Set up the required limit.
How can we simplify this?
We can divide the numerator and the denominator by n.
Do that.
What is the limit of the 1/
n
term in the denominator?
0
Find the value of
L
.
What can we conclude from this?
Since the limit is less than 1, we conclude that the series converges.
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