Here is the problem:

an = n/(1+sqrt(n))

I divided top and bottom by n

then had 1 in the numerator

and 1/n + 1/n^(1/2) in the denominator

could I think about this like it is 1/0 ?

because there is still an n in the denominator

so the sequences diverges, is this correct?

The problems with n^2 or n seem so easy but this one where it is sqrt(n) or N^(1/2) gives me trouble.

Thank you,

Keith