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Thread: help to calculate this sum

  1. #1 help to calculate this sum 
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    Can someone please help me to calculate this sum:

    Sum[POWER(1000;K)/FACT(K)] = ?

    K value is 0 to 200

    I cant calculate this in excel, too large numbers in the end...
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  3. #2  
    Forum Professor serpicojr's Avatar
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    What class are you doing this for? I'm guessing calculus 2, in which case you're doing power series right now, in which case you should have learned some way of estimating this sort of thing.


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  4. #3  
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    Im sorry if my problem is too easy to be ask in here but really...i dont know the answer. Please someone help me
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  5. #4  
    Forum Professor serpicojr's Avatar
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    I can't help you unless you let me know what you know. So I'll rephrase my question... in what context are you asking this? And how much math do you know?
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  6. #5  
    Forum Sophomore Absane's Avatar
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    Am I understanding the problem correctly?

    Evaluate 1! + 1!2! + 1!2!3! + ... + 1!2!3!...999!1000!
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  7. #6  
    Forum Professor serpicojr's Avatar
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    I thought he was asking for:

    1 + 1000/1! + 1000<sup>2</sup>/2! + ... + 1000<sup>200</sup>/200!

    I was going to say you could estimate this by e<sup>1000</sup>, but the series is truncated way too early for this to be at all useful.
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  8. #7  
    Forum Professor serpicojr's Avatar
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    Regarding the comment of yours that disappeared, I, too, was thinking Taylor remainders, but, as you just noticed, it's useless.
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  9. #8  
    Forum Sophomore Absane's Avatar
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    Quote Originally Posted by serpicojr
    Regarding the comment of yours that disappeared, I, too, was thinking Taylor remainders, but, as you just noticed, it's useless.
    I'm not sure if there is anything useful we can do other than give the approximate answer as evaluated by Mathematica or other software packages. We could give bounds, but that doesn't answer his question.
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  10. #9  
    Forum Professor serpicojr's Avatar
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    I wish this guy would tell us why he wants to calculate this. Some context would suggest what sorts of methods he has at his disposal to calculate it.
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