1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Limit Problem

  1. Apr 17, 2005 #1
    Can anyone help with these?

    1. [tex]\lim_{n\rightarrow 0}\frac{\log_{2}\sum_{k=1}^{2^n}\sqrt{k}}{n}[/tex]

    2. [tex]\lim_{n\rightarrow 0}\frac{\log_{2}\sum_{k=1}^{2^n}\sqrt{2k-1}}{n}[/tex]

    Thanks for you help.
  2. jcsd
  3. Apr 17, 2005 #2


    User Avatar
    Science Advisor
    Homework Helper

    Regarding just the first one:

    Although I question this, Mathematica returns:

    [tex]\mathop \lim\limits_{n\to 0}\frac{Ln[\sum_{k=1}^{2^n}\sqrt{k}]}{n}\approx 0.8527[/tex]

    Seems to me that it should be [itex]-\infty[/itex]

    Since once n gets below 1, the sum goes to just 1.

    How about this also too?

    [tex]\mathop \lim\limits_{n\to \infty}\frac{Ln[\sum_{k=1}^{2^n}\sqrt{k}]}{n}[/tex]

    This one Mathematica returns 1.0397 which makes sense if you plot the values for a range of n, it seems to approach a value near this.

    I'd like someone to explain these also.
  4. Apr 17, 2005 #3
    I encountered these problems on another site, and was just interested in them. I know some single-variable calculus, but I am just working on sequences and series now, so I was wondering if anyone knew of a trick to get these done.

    Thanks for your help.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Limit Problem
  1. Limit problem. (Replies: 19)

  2. A limit problem (Replies: 9)

  3. Limit problem (Replies: 2)

  4. Limit Problem (Replies: 5)

  5. Problem with limit (Replies: 4)