Answer: Diverges
This series diverges by the limit test (some books may call it the nth term test).
Recall the limit test is the idea if the sequence doesn't converge to 0, then the series diverges.
In this case, the sequence converges to n/(7n) = 1/7 since all we are about are the leading terms when n gets very large.
After some very large n value, we're effectively adding on 1/7 or very close to it, each time. The infinite sum does not approach a fixed value. It keeps growing forever.