Yet another convergence problem

  • Thread starter lmannoia
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    Convergence
In summary, "Yet another convergence problem" occurs when a mathematical or computational method does not reach a stable or accurate result after repeated iterations. This can be avoided by carefully choosing the appropriate method and tuning parameters, using smaller step sizes, and checking for convergence. Common methods for dealing with this problem include using a different method or algorithm, changing initial conditions or parameters, or using a more accurate numerical representation. In some cases, this problem can be solved by making adjustments, but it can also hinder scientific research by preventing accurate results and wasting time and resources.
  • #1
lmannoia
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Homework Statement


It's the sum (n=1 to infinity) of (n!)/(2^(n^2)) I hope that's not too hard to read?


Homework Equations


The ratio test, I think? Since it contains a factorial.


The Attempt at a Solution


It seems like I'm never short of calculus questions. Everytime I try to apply the ratio test, I end up getting to (n+1)(2^(n^2)) / (2^(n+1)^2) and I'm unsure of where to go from there to see if it converges or not.
 
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  • #2
Try expanding 2^(n+1)^2 and then rewrite that using some rules of exponents.
 

What causes "Yet another convergence problem"?

The most common cause of this problem is when a mathematical or computational method fails to converge to a solution, meaning it does not reach a stable or accurate result after repeated iterations.

How can "Yet another convergence problem" be avoided?

To avoid this problem, it is important to carefully choose the appropriate method for the problem at hand and to carefully tune any parameters involved in the calculation. Additionally, it can be helpful to use smaller step sizes and to check for convergence at each iteration.

What are some common methods for dealing with "Yet another convergence problem"?

Some common methods for dealing with this problem include using a different method or algorithm, changing the initial conditions or parameters, or using a more accurate numerical representation.

Can "Yet another convergence problem" be solved?

In some cases, this problem can be solved by making adjustments to the method or parameters being used. However, in some cases, it may not be possible to find a solution that accurately converges.

How can "Yet another convergence problem" impact scientific research?

This problem can significantly impact scientific research by preventing accurate and reliable results from being obtained. It can also lead to wasted time and resources as researchers try to find a solution to the problem.

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