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Anthony Reverri
Section 27
Workshop 13
The first part of this week’s problem asks us if a power series whose interval of convergence is
the interval (0, 1] exists. In order to find such a power series, we must find each piece of the
series one step at a time.
The definition of a power series is as follows:
C
is defined as a constant that is the “center” of the power series. Since our interval of
convergence is (0, 1], c is the point in the center of this interval:
Now let’s take a look at what we have so far:
At this point we need to find an appropriate. The best method for this situation is the “guess and
check” method. I am going to apply the ratio test to test for convergence with my initial guess for
being 1. The strategy is to make a “stab in the dark” at this problem and react to whatever
happens.
Ratio test:
By the Ratio Test if
the series converges. The absolute value will end up giving us two solutions,
which results in and interval of convergence. Let’s find the values where the equation above
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This note was uploaded on 12/05/2011 for the course MATH 152 taught by Professor Sc during the Spring '08 term at Rutgers.
 Spring '08
 sc
 Calculus, Power Series

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