# Math Help - limit of sequence?

1. ## limit of sequence?

Hi:

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.

2. Originally Posted by Rich B.
Hi:

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:

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

to me.

RonL

3. Thanks Ron.

...Rich