Which Tests Determine Convergence for These Series?

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Discussion Overview

The discussion revolves around determining the convergence of two specific series involving factorials and exponential functions. Participants seek guidance on which convergence tests to apply to these series, with a focus on mathematical reasoning and problem-solving techniques.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents two series for convergence testing, specifically asking which tests should be applied.
  • Another participant suggests that rather than asking multiple similar questions, the original poster should apply previously given help to the other problems.
  • Several participants express confusion regarding the notation used, particularly the lack of LaTeX formatting, which complicates the interpretation of the series.
  • A moderator clarifies the numbering of the problems to avoid confusion, indicating that what was referred to as #3 should actually be #6.

Areas of Agreement / Disagreement

The discussion contains some agreement on the need for clarity in notation, but there is no consensus on the specific convergence tests to be applied, as participants have not yet provided solutions or methods.

Contextual Notes

Limitations include the unclear notation used in the series, which may affect participants' ability to engage with the problems effectively. The discussion also lacks detailed mathematical steps or assumptions that could guide the convergence testing process.

Tebow15
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Test these for convergence.

5.
infinity
E...((n!)^2((2n)!)^2)/((n^2 + 2n)!(n + 1)!)
n = 0

6.
infinity
E...(1 - e ^ -((n^2 + 3n))/n)/(n^2)
n = 3

note: for #3: -((n^2 + 3n))/n) is all to the power of e

Btw, E means sum.

Which tests should I use to solve these?
 
Last edited by a moderator:
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Rather than posing a series of similar questions, you should apply the help given to you on one thread to attempt the other problems.
 
(Poolparty)
 
cacophony said:
Test these for convergence.

5.
infinity
E...((n!)^2((2n)!)^2)/((n^2 + 2n)!(n + 1)!)
n = 0

6.
infinity
E...(1 - e ^ -((n^2 + 3n))/n)/(n^2)
n = 3

note: for #3: -((n^2 + 3n))/n) is all to the power of e

What do you mean by #3 ? , maybe you meant the question you posted earlier. Not writing the sums in LaTeX makes it so difficult to interpret !
 
ZaidAlyafey said:
What do you mean by #3 ? , maybe you meant the question you posted earlier. Not writing the sums in LaTeX makes it so difficult to interpret !

Moderator note: I renumbered the problems so as to have no more than two problems in a thread. The #3 should be a #6. It's Problem #6.
 

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