Nerdy question: What is a practical application of knowing if an infinite series converges or diverges?

Full-filling my personal inquisitiveness and delight?

If you are looking for a girl that has “scientific smarts” and you mentioned this fact, then you’d be more likely to attract her, and repel the women that you aren’t looking for.

You could strike up some awesome conversations at Star Trek conventions with this kind of information, rather than just sitting around in the corner by yourself fondling your autographed pictures of William Shatner.

You’d probably find and make life long friends if you brought up this topic at your local aerospace museum or science center.

I don’t see any down sides : )

great question. I did not know the answer. so i looked it up. here’s what I found:

Infinite series are practically useful because they can be approximated by a finite series.

Take for example JPEG image compression. The changeing pattern of colours in an image can be fitted by an fourier series (in practise it is a cosine series that is used) As an infinite series could take an infinite amount of information to store it, that doesn’t seem like a good thing, but the infinite series can be approximated by the first few terms. That means that instead of keeping the image in memory you only need keep the first few terms of an infinte series – a big saving in memory. (details in source)

This is a common example – You don’t actually use the infinite series when you make a jpeg, but the people who invented jpeg couldn’t have done so without understanding series.

In general applications of fourier series are widespread in engineering. They are used in the analysis of current flow in electrical engineering. They are used analysis of sound waves. They are used in mathematics to solve differential equations. Fourier’s ideas can also be found in electronically synthesized music and talking computer chips.
Source:
http://photo.net/learn/jpeg/

Also, apparently they’re also used when studying the bouncing of a ball. If we have to find out the time it takes to come to rest, its an infinite converging series

but actually i agree with @tranquilsea :)

Well—if you know it diverges, you won’t waste time trying to calculate the sum.

Not sure if this is sufficiently practical, but certain converging sequences converge on important irrational numbers like pi and e. These are the best methods we have for calculating good approximations of these numbers.

What Mariah said. Infinite series are a necessary tool to find/understand/explain many numbers that have many practical applications.