We want to determine if the sequence $\frac{n}{3+6n}$ is monotonic.
Using the difference test we get that $s_{n+1}-s_{n} =$ < = > 0
Hence the sequence is monotone decreasing monotone increasing monotone nonincreasing monotone nondecreasing cannot be determined
The smallest number that $s_n$ is less than for every n is , hence $\lim \limits _ {n \to \infty} s_n =$