 Let's determine the convergence of the given series n equal the sum n equals 1 to infinity of 2 over the cube root of n and so take a moment to think about this on your own which Which convergence test could I use for series pause the video if necessary and think about that for a second? Now if it were me this series makes me think of a p-series This looks like a p-series and hence I want to use the p-test The reason for that is this plus 2 that sits on the top I could pull it out and then in the denominator. I have this cube root of n I could write that using an exponent and if I did that this would look like two times the sum Where n equals 1 to infinity of 1 over well the cube root of n is into the one-third power and Thus we see that it's two times a p-series the p-value is this number right here We get that p equals one-third Now for the p-test if p is greater than one the series converges But if p is less than or equal to one it'll be divergent Notice here. We're less than equal to one and so then I would conclude that this series is divergent It's divergent and this follows from the p-test