We want to determine if the sequence \frac{n}{3+6n} is monotonic.

Using the difference test we get thats_{n+1}-s_{n} =
<
=
>
0

Hence the sequence is
monotone decreasing
monotone increasing
monotone nonincreasing
monotone nondecreasing
cannot be determined

The smallest number thats_n is less than for every n is , hence
\lim \limits _ {n \to \infty} s_n =

Using the difference test we get that

Hence the sequence is

The smallest number that

You can earn partial credit on this problem.