Determine whether the series is convergent or divergent:
The sum from n=1 to infinity of the series 1/(5n+2).
I used the divergence test -- lim(n->inf) of 1/(5n+2) -> infinity, therefore, not divergent.
But if I integrate,
The integral from 1 to inf of 1/(5x+2) dx ; lim(t->inf) of the integral of 1 to t of 1/(5x+2) dx, use u substitution, etcetera, to come out with
(1/5) lim(t->inf) of ln|5t+2| - ln|7|, which is of course infinity.
Am I just not understanding something here?