Last of a series (correction of previous post)

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Discussion Overview

The discussion revolves around the convergence of two mathematical series involving factorials and trigonometric functions. Participants explore the nature of these sums and share insights on software and hardware for mathematical computations.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant requests assistance in finding the values of two series involving cosine and sine functions, indicating a lack of computational skills.
  • Another participant questions the convergence of the series, suggesting that there is no apparent reason for them to converge.
  • A subsequent post asserts that both sums do not converge, expressing a negative outlook on their behavior.
  • Visual representations of the partial sums for both series are provided, although their implications on convergence are not discussed further.
  • Several participants inquire about affordable hardware and software options for performing mathematical calculations, indicating a need for accessible tools.
  • One participant shares their experience with a low-cost PC and discusses the potential for educational discounts on software.
  • Another participant suggests attending tech shows for better deals on math software, highlighting the variability in pricing based on educational affiliation.

Areas of Agreement / Disagreement

Participants express disagreement regarding the convergence of the series, with some asserting non-convergence while others question it without reaching a consensus.

Contextual Notes

The discussion lacks detailed mathematical justification for the claims about convergence and does not resolve the implications of the provided visual data on the series.

Who May Find This Useful

This discussion may be of interest to individuals exploring series convergence in mathematics, as well as those seeking affordable computational tools for mathematical analysis.

Loren Booda
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Would you find the values of

[oo]
[sum] (-1)ncos(((2n)!)1/(2n))
n=1

and

[oo]
[sum] (-1)n+1sin(((2n+1)!)1/(2n+1))
n=0

for me? I am computer-challenged.
 
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Are you sure that they converge?

From a first glance, I can see no reason why they should.
 
The 2 sums don't converge...:frown:
 
Picture of partial sums for the cos sum...
http://www.angelfire.com/pro/fbi/xcos.bmp

Picture of partial sums for the sin sum...
http://www.angelfire.com/pro/fbi/xsin.bmp
 
Last edited by a moderator:
What sort of hardware/software do you guys use to work out these problems? Could you suggest some simple, inexpensive ware for math?

I'm sticking with the two constants, "L" and "B," that bogdan confirmed previously.
 
A 486 PC...or something like that...It costs somewhere between 50 and 100 dollars...
 
Is there any easily learned, inexpensive yet versatile math software out there that I could run on my PC?
 
Inexpensive Math Software

Inexpensive depends on what you're willing to pay for it. If you are affiliated with a college you may get an educational version of the software that would be much, much cheaper than the full blown versions, even get the full blown version at an academic price.

Otherwise, I think you are going to pay full price and that is expensive. The other option is to attend the computer/tech shows that seem to make the circuit of civic centers during the summer. I have seen some good prices on math software if you can find it.

Good luck.

Ken
 

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