Convergence or Divergence of ∑ tan(1/k) for k=5

[cloveryeah]

Homework Statement

∞
∑ tan(1/k)
k=5

show that it is convergent or divergent

Homework Equations

The Attempt at a Solution

i used ratio test, but it's equal to 1, it means no works...
i used divergence test, it equals to 0, no work too...
so what should i do? i don't know how to use comparision test to attempt this problem

 

[mfb]

What is tan(0.001)? tan(0.0000001)? Do you see some function that looks similar and could be used for comparison?

 

[pasmith]

Use the result that if $0 < x \leq \frac12\pi$ then $\sin x \geq \frac{2x}{\pi}$ to show that $$\tan\left(\frac1k\right) \geq \frac{2}{\pi k}.$$