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Math Help - does this sum exist?

  1. #1
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    does this sum exist?

    Could someone please help me to show whether or not the sum from k=1 to infinity of 1/2k exist or doesn't exist.
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  2. #2
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    Quote Originally Posted by ravenboy View Post
    Could someone please help me to show whether or not the sum from k=1 to infinity of 1/2k exist or doesn't exist.
    \sum_{k=1}^{+\infty} \frac{1}{k} is the famous harmonic series (Google it).
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  3. #3
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    it doesn't.

    see http://en.wikipedia.org/wiki/Harmoni...s_(mathematics).

    (ahh, got beaten.)
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  4. #4
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    basically i am trying to prove the sum of k=1 to infinity of 1/(K+ sqrt(k)) doesn't exist.
    i know the sequence is greater than or equal to 1/2k and 1/2k doesn't exist so by comparison test our sequence doesn't exist.
    how would you show 1/2k doesn't exist? Is it because:
    we know 1/k doesn't exist and so 1/2k is just (1/2)*(1/k) so 1/2k doesn't exist.
    Am i right in, saying we cant use comparison test to show 1/2k doesnt exist compared to 1/k because (1/2k)<(1/k). thanks for your help thus far.
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  5. #5
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    Quote Originally Posted by ravenboy View Post
    basically i am trying to prove the sum of k=1 to infinity of 1/(K+ sqrt(k)) doesn't exist.
    i know the sequence is greater than or equal to 1/2k and 1/2k doesn't exist so by comparison test our sequence doesn't exist.
    how would you show 1/2k doesn't exist? Is it because:
    we know 1/k doesn't exist and so 1/2k is just (1/2)*(1/k) so 1/2k doesn't exist. Mr F says: Yes.

    Am i right in, saying we cant use comparison test to show 1/2k doesnt exist compared to 1/k because (1/2k)<(1/k). thanks for your help thus far. Mr F says: Why would you be trying to do this when your previous argument is fine ....
    ....
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  6. #6
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    thanks. wasn't sure if the following bit
    ""1/k doesn't exist and so 1/2k is just (1/2)*(1/k) so 1/2k doesn't exist."
    was true or not as lecturer didn't really explain that bit, So i was assuming that was true. Thanks again.
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  7. #7
    Super Member redsoxfan325's Avatar
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    Any nonzero constant multiple times a sum doesn't change whether it converges or not.
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