Ok so I'm working on this problem but have problem understanding it. I got the right answer but I made an assumption to get there. I need help proving that assumption.

Here is the problem

Find the values of p for which the series in convergent

Ok so I used the integral test because f(x) = is continous, positive, and decreasing(this is where I made the assumption that it was decreasing).

Thus the limit exist when so the series converges when p< -1.

Is that right? Also how do I show that the function is decreasing(the assumption I need to prove). I took the 1st derivative and equalled it to less than 0 to show me where it was decreasing but ran into problems.

This is what I get stuck on with the derivative

Thanks