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Series and sequence help

  1. Nov 21, 2005 #1
    hi everyone, im having trouble with a few problems, i was wondering if anyone can help me thank.
    1.) given r= 11/22

    a.)consider the sequence {nr^r}. if convergent find limit. if divergent find if it goes to inf or minus inf. or div otherwise
    lim nr^r = ?

    b.)take my word for it that it can be shown that
    sigma i=1 to n ir^i = (n(r^(n+2))-(n+1)(r^(n+1))+r)/((1-r)^2)

    now consider the series sigma n=1 to infinity nr^r
    sigma n=1 to infinity nr^r = ?

    2.) An= 8n/(6n+13)
    the series sigma n=1 to infinity (An) =?
    if convergent, find sum. if divergent find it it goes to positive or negitive.

    and 3.) An= 50/(5^n)
    find whether {An} is convergent, if so, find limit.

    any help would be great. thanks.
  2. jcsd
  3. Nov 22, 2005 #2


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    Gold Member

    You mean r=0.5?
    If r=0.5, then what's [tex] \lim_{n\rightarrow \infty} n \sqrt{0.5} [/tex]
    You have lost me here. If r=0.5, how is the series convergent in the first place?
    What does the divergence test tell you?
    You have already stated how to find if a sequence is convergent or divergent. Why not apply it here?
    Last edited: Nov 22, 2005
  4. Nov 22, 2005 #3
    sorry for the first one a.) and b.) instead or nr^r i meant nr^n

    ok for 2.) i got infinity

    and 3.) would go to minus infinity so would it be divergent?
    Last edited: Nov 22, 2005
  5. Nov 22, 2005 #4
    i still need help on 1a and b and 3, anyhelp would be good, thanks.:smile:
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