calculus problem?

Question

determine if the series from 1 to infinity [10/(4n + 7ln(n) - 5)] converges or diverges.

I tried using a comparison test of 10/4n, but that is a p-series = 1 which diverges, and it is greater than the original so it doesn't help

Answer 1

First, work out what you think will happen; 4n is the dominant term on the bottom, so we do expect it to diverge.

You could use a ratio test with 10/4n, but you can still do this with a comparison test: note that ln n < n, so 4n + 7 ln n - 5 < 4n + 7n - 5 = 11n - 5 < 11n. So 10/(4n + 7ln(n) - 5) > 10/(11n) and we know 10/(11n) diverges.