Is this series absolutely convergent, conditionally convergent, or divergent?

Sum from n=1 to infinity of (-1) ^ n * [ (3^n)/(2^n + 3^n) ] ?

Question

Is this series absolutely convergent, conditionally convergent, or divergent?

Sum from n=1 to infinity of (-1) ^ n * [ (3^n)/(2^n + 3^n) ] ?

anonymous · Answer

$$\sum_{n=1}^{\infty} (-1)^{n} \frac{ 3^{n} }{ 2^{n} + 3^{n} }$$

I tried using the ratio test, but it does not seem to work?

anonymous · Answer

jeez this is tricky
it looks like there might be two different limits depending on whether n is even or odd
so it seem unlikely that it converges

anonymous · Answer

i can't get a good idea of what the partial sums are
maybe there is some other method that shows it diverges

anonymous · Answer

Will the limit comparison work? I tried to compare it to $$\sum_{n=1}^{\infty} \frac{ 3^{n} }{ 3^{n} } = \sum_{n=1}^{\infty} 1$$ which diverges, but then finding the limit of a_n/b_n is tricky.

anonymous · Answer

no i don't think so
i am stumped

anonymous · Answer

i think the limit of the terms (not the sum) is not zero, but is one

anonymous · Answer

How are you able to determine that?

anonymous · Answer

i posted it as a question

anonymous · Answer

http://openstudy.com/study#/updates/51872f82e4b05b0712667c12