calculus - Determining whether the series: $sum_{n=1}^{infty} tanleft(frac{1}{n}right) $ converges

I was tasked with determining whether the following series:

$$\sum_{n=1}^{\infty} \tan\left(\frac{1}{n}\right) $$

converges.

I tried employing the integral test which failed and produced incalculable integrals. Other methods didn't prove effective also. I was suggested that the Maclauren series might be of use here, but I'm not sure how to employ it.

Answer

Or by limit comparison test with $\sum\frac1n$ since by standard limit for $x\to 0\implies\frac{\tan x}{x}\to 1$ and then

$$\frac{\tan\left(\frac{1}{n}\right)}{\frac1n}\to1$$