Determine whether or not the series is convergent or divergent. If it is convergent, find its sum. 1) 1/3 + 1/6 + 1/9 + 1/12 + 1/15 + ... inf. 2) E (n-1)/(3n-1) n=1 Okay, I'm having trouble with determining the convergence/divergence. My book states that, "If the series inf. E Asubn n=1 is convergent, then lim as n goes to inf. asub n=0." and it also states that, "If lim as n goes to inf. asubn does nto exist or if lim as n goes to inf. does not equal 0, then the series inf. E Asubn n=1 is divergent. ---- Here's where I'm having trouble. I set up the sum series for the first question as: inf. E Asubn 1/(3n) n=1 Then I took the limit as n goes to inf. of 1/(3n) and got 0. So by the book, wouldn't this make it convergent? However my book has the answer as being divergent. Then for the second question, I took the limit as n goes to inf. of (n-1)/(3n-1) to be 1/3. So wouldn't this make it convergent as well? The book has the answer as being divergent. If someone would articulate the convergent/divergent test a little better it would be greatly appreciated. Thanks!