General Contents
Detailed Contents
Index
Programmed tutorial: p-Series Test of Convergence or Divergence of a Series: Example 1
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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.
Determine whether the series
converges or diverges.
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?
No, the partial sums appear to be increasing.
What type of series might this be?
Let’s see if it is a
p
-series.
What is the form of the general term of a
p
-series?
In order to convert to this form, we need to replace the cube root with a power.
What is the power?
The cube root is the same as the
1
/
3
power.
Write the general term of the given series.
So, this is a
p
-series.
Does it converge?
No.
Why?
A
p
-series converges only if p > 1.
Does this agree with our diagrams above?
Yes.
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