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Math Help - Infinite Series and Limits

  1. #16
    Senior Member roninpro's Avatar
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    I didn't see this addressed anywhere: has anyone checked that this limit even exists? I tried evaluating it numerically, and it seems to grow without bound.
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  2. #17
    Junior Member
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    Hi I think because the limit does not exist, we need to use improper integral for it too. So its loosely speaking a combo of riemann sum and improper integral.
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  3. #18
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    Quote Originally Posted by metallicsatan View Post
    This was a problem in my test this morning. I was not able to answer it. But I thought it was pretty interesting, and would like to know the answer. Could you guys help me out?

    \displaystyle \lim_{k \to \infty}\sum_{n=1}^k \frac{n^2}{n^2+k^2}
    I think there might be a typo in the question. LOL could be be the original numerator is n instead of n^2? that makes it solveable and the problem of an extra k will be solved too.
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  4. #19
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    Quote Originally Posted by ineedyourhelp View Post
    I think there might be a typo in the question. LOL could be be the original numerator is n instead of n^2? that makes it solveable and the problem of an extra k will be solved too.

    That's my opinion, too: there's a mistake, or perhaps more, in the question as given. Either in the given expression or in the indexes, or both.

    Perhaps, though, there isn't a mistake...who knows.

    Tonio
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