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Thread: Number e

  1. #1 Number e 
    Forum Masters Degree thyristor's Avatar
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    Hi!
    I'm very curious about how you prove the following:

    I know of a calculus proof where you use L'H˘pital's rule, so I'm not interested in having this proof presented to me.
    Does anybody know of any other proof, to which they can refer?


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  3. #2  
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    I thought e was ? Honestly not sure if it is also that limit, but it has interested me to look it up.


    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

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  4. #3  
    Forum Masters Degree thyristor's Avatar
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    That can't be true since
    Your sum doesn't converge as you add 1 for each iteration and can never be negative.

    You probably mean
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  5. #4  
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    It's just .
    "There is a kind of lazy pleasure in useless and out-of-the-way erudition." -Jorge Luis Borges
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  6. #5  
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    Let's not jump all over people for making simple Tex errors.
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  7. #6  
    Forum Masters Degree thyristor's Avatar
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    Quote Originally Posted by Chemboy
    It's just .
    Well, what I wrote isn't wrong, it's just a more (unnecessarily) complicated way to express it, which I fully agree to.
    However, I would like to see the proof of what I wrote in my first post.
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  8. #7  
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    See Rudin, "Principles of Mathematical Analysis", i.e., the little blue book.
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  9. #8  
    Forum Masters Degree thyristor's Avatar
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    Where can I find that book, do you suppose?
    Do you think it is possible that one can find it in an average-sized library?
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  10. #9  
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    Quote Originally Posted by thyristor
    Where can I find that book, do you suppose?
    Do you think it is possible that one can find it in an average-sized library?
    It is still in print, but rather expensive if you buy it new. But you can usually find a copy on the used book market of past editions, which are quite sufficient, for a reasonable price. Try Alibris.com
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  11. #10  
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    Quote Originally Posted by thyristor
    Where can I find that book, do you suppose?
    Do you think it is possible that one can find it in an average-sized library?
    I doubt it. You'll need to go to a math library at a university. With any luck, it will be on reserve.

    Btw, always give wikipedia a try when it comes to looking up proofs of this nature. I'm often pleasantly surprised.

    Another thing you can do is simply enter the topic into a google search and see what comes up. Often some professor or teaching assistant somewhere has written a short exposition on the topic you're interested in, and posted it as a pdf on their website. Of course, you have to be clever about what you enter as your search parameter, but after some practice, you'll find you're able to look up a lot of math this way.
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  12. #11  
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by thyristor
    Where can I find that book, do you suppose?
    Do you think it is possible that one can find it in an average-sized library?
    It is still in print, but rather expensive if you buy it new. But you can usually find a copy on the used book market of past editions, which are quite sufficient, for a reasonable price. Try Alibris.com
    Here are the results of a couple of searches for the book.

    http://www.abebooks.com/servlet/Sear...ts=t&x=80&y=13

    http://www.alibris.com/booksearch?qw...*listing*title

    It is a very good text and well worth your trouble to purchase it. That same comment applies to all of Rudin's books, particularly Real and Complex Analysis and Functional Analysis. His Fourier Analysis on Groups is excellent, a true classic, but a bit specialized and expensive, and you need at least the basics of functional analysis to follow it. The other books that he has written are much more specialized.
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  13. #12  
    Forum Masters Degree thyristor's Avatar
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    Thanks!
    Just one question, how come the book only costs 1.00 ž on the first website?
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  14. #13  
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    Quote Originally Posted by thyristor
    Thanks!
    Just one question, how come the book only costs 1.00 ž on the first website?
    It is an international edition being sold by a company in India.
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