How do you use the limit comparison test to determine if $Sigma tan(1/n)$ from $[1,oo)$ is convergent or divergent?

Question

39948 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-09T12:11:04

$sum tan(1/n)$ is divergent.

Let $a_n= tan(1/n)$ and $b_n=1/n$ .

Let us check the hypotheses of Limit Comparison Theorem.

By l'Hospital's Rule,

$=lim_(n to infty)(sec^2(1/n)cdot cancel(-1/n^2)) /cancel(-1/n^2)=sec^2(0)=1$

Since $sum b_n$ is a harmonic series (divergent), by Limit Comparison Test, we can conclude that $sum tan(1/n)$ is also divergent.

I hope that this was clear.

How do you use the limit comparison test to determine if Sigma tan(1/n)Sigma tan(1/n) from [1,oo)[1,oo) is convergent or divergent?