Proving the divergence of arcsin(1/n)

[mybluesock]

Homework Statement

Is $$\sum$$(-1)^(n-1)*arcsin(1/n) absolutely convergent, conditionally convergent, or divergent?


2. The attempt at a solution

The original function is alternating, so by the alternating series test, the function is convergent, because 0 < arcsin(1/(n+1)) <arcsin(1/n), and the limit of arcsin(1/n)=0.
So that rules out divergent. To determine whether the series is absolutely or conditionally convergent, you test the convergence of the absolute value of the series, which would be $$\sum$$ arcsin(1/n). However, I'm not sure what test to use now. Should I use the comparison test, and if so, what should I compare it to?

 

[lanedance]

i would attempt to use a comparison test...

considering the taylor series of arcsin will also be useful in showing the comparison is valid