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Infinite Series ?COnverge or Diverge

  1. May 20, 2010 #1
    Infinite Series!!??COnverge or Diverge

    1. The problem statement, all variables and given/known data
    1.
    ∑(infinity, k=1) 5k^(-3/2)

    2.
    ∑(infinity, k=1) 1/(k+3)
    2. Relevant equations
    converge or diverge

    3. The attempt at a solution
    1. converges p=3/2... 5/(infin)=> 0
    2. diverges p=1
    I still don't get why 2 diverges? 1 converges b/c it gets to 0??
     
  2. jcsd
  3. May 20, 2010 #2

    lanedance

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    Re: Infinite Series!!??COnverge or Diverge

    use integral test for 1

    for 2 try and find a comparison test with a harmonic series(1/k)
     
  4. May 20, 2010 #3
    Re: Infinite Series!!??COnverge or Diverge

    Umm, I am not supposed to use those tests...

    Is there any other method??
     
  5. May 20, 2010 #4
    Re: Infinite Series!!??COnverge or Diverge

    Can't you just use the test for divergence for #2?

    EDIT: I think it works for both #1 and #2.
     
  6. May 20, 2010 #5
    Re: Infinite Series!!??COnverge or Diverge

    could you please show me?thanks
     
  7. May 21, 2010 #6
    Re: Infinite Series!!??COnverge or Diverge

    The best that I can do is tell you what the Test for Divergence is.

    The Test for Divergence states that:

    If [tex] lim _{x\rightarrow\infty} a_{n} \neq 0, \sum a_{n} diverges. [/tex]

    P.S. My LaTeX is weak, could someone tell me how to add spaces?
     
  8. May 21, 2010 #7

    lanedance

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    Re: Infinite Series!!??COnverge or Diverge

    what can you use? i can't read your question/notes/teachers mind ;)
     
  9. May 21, 2010 #8

    lanedance

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    Re: Infinite Series!!??COnverge or Diverge

    i think both the terms go to zero in the limit? so it doesn't show divergence?

    as for latex, just found out myself (from other posts)-, you can also add the slash to make the limit show correctly, have a look at these:
    single space "\"
    [tex] \lim _{x\rightarrow\infty} a_{n} \neq 0, \ \sum a_{n} \ diverges. [/tex]

    multispace 0.5 inches "\hspace{0.5 in}"
    [tex] \lim _{x\rightarrow\infty} a_{n} \neq 0, \hspace{0.5 in} \sum a_{n} \ diverges. [/tex]

    using itex (inline tex) and splitting into 2 parts
    [itex] \lim _{x\rightarrow\infty} a_{n} \neq 0[/itex], [itex]\sum a_{n} \ diverges. [/itex]
     
    Last edited: May 22, 2010
  10. May 21, 2010 #9
    Re: Infinite Series!!??COnverge or Diverge

    what are you talking about? #1 converges and #2 does diverge but you're not going to show it using the divergence test since [itex]lim_{k\rightarrow \infty} \frac{1}{(k+3)} = 0[/itex]

    to op:

    for #1 it's a p series
    for #2 show that it's bigger than [tex]\sum \frac{1}{5k}[/tex] and then show that that diverges
     
  11. May 22, 2010 #10
    Re: Infinite Series!!??COnverge or Diverge

    Wow, I apologize to the OP. Guess I should stop doing math at 4 am and just go to bed! Sorry for any confusion, I definitely see my blindingly obvious mistakes now.
     
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