# Convergence or divergence

1. Apr 26, 2015

### cloveryeah

1. The problem statement, all variables and given/known data

∑ tan(1/k)
k=5

show that it is convergent or divergent

2. Relevant equations

3. 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 dont know how to use comparision test to attempt this problem

2. Apr 26, 2015

### Staff: Mentor

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

3. Apr 26, 2015

### pasmith

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