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Math Help - How to determine convergence/divergence of negative functions?

  1. #1
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    How to determine convergence/divergence of negative functions?

    My teacher said that -1/n diverges simply because it is the opposite of the harmonic series 1/n but I was wondering if there were any tests you could do to prove this. I know for -1/n^2 you know it diverges because you can take the absolute value and prove absolute convergence but you can't do that for -1/n. I thought about the integral test which seems to work as -ln(n) diverges but is there a different test I can use? I'm just a little confused about how to approach negative functions. Thanks!
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  2. #2
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    Re: How to determine convergence/divergence of negative functions?

    Also, for the nth term test, if you use that on a negative function and get a negative value, does that mean the function diverges? For example, -n^2/(n+1)
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  3. #3
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    Re: How to determine convergence/divergence of negative functions?

    If lim(an)=L then lim(kan)=kL where k is a constant
    k=-1 and an​=1/n in your case. Since the limit L diverges kL will also diverge.
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  4. #4
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    Re: How to determine convergence/divergence of negative functions?

    so basically any series that diverges will diverge if it's negative too?
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