Series using comparison test The series is as shown
$$\sum\limits_{n=1}^\infty\dfrac{\tan(1/n)}{n^{0.5}}$$
Using P-series, 0.5<1 therefore it is divergent
$$\frac{1}{n^{0.5}}$$
It appears that i can't use P-series
What test should i use if this is wrong as it should converge rather than diverge

Don't be too hasty! For large $n$, $\tan(1/n) \sim 1/n$, where $\sim$ means that the two are asymptotic as $n$ approaches $\infty$. As $n$ increases, your whole summand is asymptotic to $1/n^{(3/2)}$. I think your series actually converges.
This is a heuristic argument, though it could probably pass in a Calc 2 course.
