Proving Convergence of Two Sums at 0

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Homework Help Overview

The discussion centers around proving the convergence of two specific sums, namely the sum of e^(n^2)*x^n and the sum of e*n^(n)*x^(n), with the assertion that they only converge at x=0. The subject area involves series convergence and power series analysis.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the application of the ratio test for power series and question the formulation of the sums, particularly regarding the presence of division or negative signs in the exponents. There is also a focus on understanding the implications of the original poster's statement about convergence.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the original problem statement and exploring the correct formulation of the series. Some guidance has been offered regarding the ratio test, but no consensus has been reached on the specifics of the sums.

Contextual Notes

There is uncertainty regarding the correct representation of the sums, with participants questioning whether any signs or divisions are missing in the original poster's statement. This ambiguity may affect the analysis of convergence.

tbone413
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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)


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 don't know much about it.


The Attempt at a Solution

 
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Whart you are talking about is the "ratio test" for power series. What is An+1/An for these series?
 
tbone413 said:

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...
 
dynamicsolo said:
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.
 
HallsofIvy said:
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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