(New page: Category:MA425Fall2009 ==Discussion area to prepare for Exam 2== [http://www.math.purdue.edu/~bell/MA425/prac2.pdf Practice Problems for Exam 2]) |
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[http://www.math.purdue.edu/~bell/MA425/prac2.pdf Practice Problems for Exam 2] | [http://www.math.purdue.edu/~bell/MA425/prac2.pdf Practice Problems for Exam 2] | ||
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| + | To find the radius of convergence of <math>\sum_{n=0}^\infty (n!)z^{n!}</math>, you'll need to use the Ratio Test. | ||
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| + | <math>\frac{u_{n+1}}{u_n}=\frac{(n+1)!z^{(n+1)!}{n!z^{n!}=(n+1)z^{n\cdot n!</math>. | ||
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| + | Ask yourself what that does as n goes to infinity in case |z|<1, =1, >1. | ||
Revision as of 06:50, 13 November 2009
Discussion area to prepare for Exam 2
To find the radius of convergence of $ \sum_{n=0}^\infty (n!)z^{n!} $, you'll need to use the Ratio Test.
$ \frac{u_{n+1}}{u_n}=\frac{(n+1)!z^{(n+1)!}{n!z^{n!}=(n+1)z^{n\cdot n! $.
Ask yourself what that does as n goes to infinity in case |z|<1, =1, >1.
