[Community Question] Calculus: Calculus 1: limit of sum

One of our user asked:

I'm studying for my calculus 1 exam and came across this sample question from the professor's collection:

Calculate: $\lim\limits_{n\ \rightarrow\ \infty} \frac{1}{2\log(2)}+\frac{1}{3\log(3)} + \dots + \frac{1}{n\log n}$ (hint: separate into blocks)

Unfortunately the sample questions don't include answers and I'm at a loss as to how to proceed; I'd really appreciate some help.

Thanks!