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Math Help - limit of sequence?

  1. #1
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    limit of sequence?

    Hi:

    Would someone please help me interpret the following?

    L=lim (sqrt(1)+sqrt(2)+......+sqrt(n))/n^(1.5) where n--->infinity.

    Is the variable "n" just the term number. That is, because all terms in the sum are divided by n^(1.5), do we interpret this as:

    [sqrt(1)]/1^1.5 + sqrt(2)]/2^1.5 + sqrt(3)]/3^1.5 +...= 1/1+1/2+1/3+...
    which, of course, is a divergent harmonic series.

    Or, is it the limit of (1^ 0.5 + 2^ 0.5 + 3^ 0.5 + ... +n^ 0.5), all divided by the cube of the very last term; n-->infinity?

    I prefer that you not solve the problem. I just wish to know how to read it.

    Thanks,

    Rich B.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Rich B.
    Hi:

    Would someone please help me interpret the following?

    L=lim (sqrt(1)+sqrt(2)+......+sqrt(n))/n^(1.5) where n--->infinity.

    Is the variable "n" just the term number. That is, because all terms in the sum are divided by n^(1.5), do we interpret this as:

    [sqrt(1)]/1^1.5 + sqrt(2)]/2^1.5 + sqrt(3)]/3^1.5 +...= 1/1+1/2+1/3+...
    which, of course, is a divergent harmonic series.

    Or, is it the limit of (1^ 0.5 + 2^ 0.5 + 3^ 0.5 + ... +n^ 0.5), all divided by the cube of the very last term; n-->infinity?

    I prefer that you not solve the problem. I just wish to know how to read it.

    Thanks,

    Rich B.
    Looks like:

    <br />
L=\lim_{n \to \infty} \left(\frac{\sqrt{1}+\sqrt{2}+......+\sqrt{n}}{n^{  1.5}}\right)<br />

    to me.

    RonL
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  3. #3
    Member
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    Wethersfield, CT
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    Thanks Ron.

    ...Rich
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