limit of sequence?

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March 17th 2006, 02:09 AM
Rich B.

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.
March 17th 2006, 02:54 AM
CaptainBlack

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
March 17th 2006, 03:30 AM
Rich B.

Thanks Ron.

...Rich