Question

Determine whether the sequence converges or diverges. If it converges, find the limit. An=n/(1+ sqrt(n))

Answer 1

use nth term test (also called Divergence Test)
if
\[\Large \lim_{n \rightarrow \infty} a_{n} \ne 0\]
then series is divergent
so
\[\Large \lim_{n \rightarrow \infty} \frac{n}{1+\sqrt{n}}\]
can you find this Limit ?

Answer 2

it goes to infinite right?

Answer 3

yes correct .
so it means the series is .............. ?

Answer 4

divergent

Answer 5

yes thats correct !

Answer 6

thanks!

Answer 7

:) you are welcome !