Question

determine whether the sequence converges or diverges: ln(n)/(n)^1/2... I have 2(n)^1/2 divided by n. But now what??

Answer 1

simplify and take limit.

Answer 2

Use L'Hospital's rule for
\[
g(x) = \frac{\ln (x)} {\sqrt x}
\]

Answer 3

you get
\[
\frac { \frac 1 x}
{-\frac 1 { 2 \sqrt x}}= - \frac 2 {\sqrt x}
\]
which goes to zero a x go to Infinity.

Answer 4

Oh yeah, I was wondering why you have 2/(x)^1/2 instead of \[2\sqrt{x} \div x\]

Answer 5

yes

Answer 6

Do you undersatnd it now?

Answer 7

I was asking why should I have \[2\div \sqrt{x} \] and not \[2\sqrt{x}\div x\]. They are different see?

Answer 8

They are the same
\[
\frac {2 x^{1/2}} {x}= \frac {2}{x^{1-\frac 12 }} = \frac {2}{\sqrt x}
\]

Answer 9

ok, thank you!!