Determine whether the series is convergent or divergent. If convergent, find its sum:

1/3 + 2/9 + 1/27 + 2/81 + 1/243 + 2/729 + ...

Not really sure how to show divergence on this. Normally I'd divide the 2nd by the 1st to find ar/a=r but it seems to fluctuate within the sequence.

Just separate into two series for n even and n odd. Both of them have an r less than 1, so both converge and hence the overall formula will converge (to the sum of their limits).

even: 2 / 3^n
odd: 1/ 3^n