To make up the power series with radius of convergence equal to one of the numbers
Explanation of Solution
Given:
The power series with radius of convergence.
Calculation:
An expression of the form
is a power series centred at
The convergence theorem for power series-
One possibility for
There is a positive number R such that the series diverges for
Now students of my group make series like this-
Student 1- radius of convergence is 1.
Since, this is an infinite geometric series, hence it converges only for, and hence radius of convergence is 1.
Student 2- radius of convergence is 2.
Since, this is an infinite geometric series, hence it converges only for, and hence radius of convergence is 2.
Similarly, other students made other series.
Now students of the other group made series like this-
Student 1- radius of convergence is 1.
Since, this is an infinite geometric series, hence it converges only for, and hence radius of convergence is 1.
Student 2- radius of convergence is 2.
Since, this is an infinite geometric series, hence it converges only for, and hence radius of convergence is 2.
Similarly, other student made the series.
Now the radius of convergence for the students was matched.
Chapter 10 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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