calculus - Limit of a set of fractions

I'm having trouble with this particular exercise in limits, and I just can't seem to find a way to crack it.

I saw a similar exercise online where they used integrals, but it's pretty early in the course so we're only supposed to use basic limit arithmetics and the Squeeze theorem (Oh boy, and I thought it had a bad name in MY language). That said, I already tried the Squeeze theorem and it doesn't work.

$$\lim_{n\to\infty} \left( \frac{1}{1\cdot4}+\frac{1}{4\cdot7}+...+\frac{1}{(3n-2)(3n+1)} \right)$$

What am I missing?

Thanks in advance.