Consider the series sum(5^n/((8n+2)(2^(n+1))),n=1 to infinity. Determine whether the series converges or diverges and state why.

Question

anonymous · Answer

Ratio Test concludes that the series diverges.

anonymous · Answer

Is that because the ratio test results in the form infinity/infinity?

anonymous · Answer

No, take the limit as n-> infinity of the absolute value of the ratio a_(n+1)/a_n and you'll get something greater than 1, which means the series diverges.

anonymous · Answer

Oh yah. That's right. I got 40/16, which is obviously greater than 1. Gosh I hate all these little rules for series. :-P

anonymous · Answer

You're also taking a course on real analysis, aren't you?

anonymous · Answer

No. It's Math 21C at UC Davis. It covers the last half of Calculus II and the first part of Calculus III.