Question

The divergence test applied to the series ∑n=1 to ∞ 3n/(8n+9) tells us that the series converges or diverges?

I got that it was divergent because it was undefined at infinity, is my answer right?

Answer 1

well, 3n/(8n+9) -> 3/8 as n->∞, so if that's what you meant to say, then you're off.

But the series clearly diverges, since the terms do not tend to zero.