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Math Help - series convergence / divergence

  1. #1
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    series convergence / divergence

    My question is a bit more general... I'm in calculus 2 now working through the chapter on finding whether or not a series converges. Many of the tests don't even tell you what a series converges to, just the fact that it does (or doesn't). It's neat and all, but I'm curious, is there a point to this?

    Back in algebra, we learned how to do fraction decomposition. It's neat and all, but seemed mostly pointless. It wasn't until Calculus 2 that I realized fraction decomposition is extremely important in taking integrals of a lot of different functions, which in turn is useful for finding areas under curves or in rotated curves. I'm just wondering if this series convergence/divergence has some sort of future importance or not.
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  2. #2
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    Re: series convergence / divergence

    Quote Originally Posted by satis View Post
    My question is a bit more general... I'm in calculus 2 now working through the chapter on finding whether or not a series converges. Many of the tests don't even tell you what a series converges to, just the fact that it does (or doesn't). It's neat and all, but I'm curious, is there a point to this?
    Pointless? If we know that a series diverges then it is really stupid of try to find it sum when we know it does not have one.
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  3. #3
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    Re: series convergence / divergence

    Ok, fair enough. I'm just not sure that finding the sum of an infinite series is really helpful outside of in a purely academic environment, but I've been very wrong before, so was just wondering if more advanced math made greater use of this idea than I was aware of. It doesn't really matter... I need to learn this to get to Calculus 3 if nothing else. For some reason it's a lot more interesting to me if there are other, more concrete applications.
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