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Power Series

  • Thread starter tbone413
  • Start date
7
0
1. Homework Statement
Prove that the following sums only converge at 0.
sum of: e^(n^2)*x^n , and
sum of: e*n^(n)*x^(n)


2. Homework Equations
well i know series converge if the lim as n approaches inf of the abs(x-c) is less than (An/An+1) but I have no idea how to prove it, I saw these for the first time yesterday in class, and dont know much about it.


3. The Attempt at a Solution
 

Answers and Replies

HallsofIvy
Science Advisor
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Whart you are talking about is the "ratio test" for power series. What is An+1/An for these series?
 
dynamicsolo
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1. Homework Statement
Prove that the following sums only converge at 0.
sum of: e^(n^2)*x^n , and
sum of: e*n^(n)*x^(n)
Are you missing either division signs or negative signs in exponents somewhere? I don't see how these are going to converge to zero as you've written them...
 
HallsofIvy
Science Advisor
Homework Helper
41,732
893
Are you missing either division signs or negative signs in exponents somewhere? I don't see how these are going to converge to zero as you've written them...
He didn't say they converge to 0, he said they only converge at x= 0.
 
dynamicsolo
Homework Helper
1,648
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He didn't say they converge to 0, he said they only converge at x= 0.
Sorry, missed the 'only'; I've read too many sentences with wrong prepositions lately and thought the OP meant 'to'. (Your mentioning the Ratio Test reinforced this...)

The first question might be: how do you write the power series for these exponential functions? What do you get when you multiply them by x^n?
 

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