Spherically Symmetric charge distribution

[TheWire247]

I am currently doing a past paper question for my electromagnetism exam and I can't seem to figure out this problem, it is probably quite simple but I can't see a solution

Homework Statement

Consider a spherically symmetric charge distribution:

ρ(r) = ρ₀(r/r₀)^-n for r>r₀

ρ(r) = ρ₀ for r≤r₀

where ρ₀, r₀ and n are constants and r = |r|

i) For which values of n is the total charge Q finite? compute the total charge for these values

Homework Equations

As above in the question

The Attempt at a Solution

I have no idea how to start

 

[Krappy]

The total charge is finite if the charge for r>r₀ is finite.

That charge is given by Q(r>r₀) = ∫ρ(r) dV = 4π∫ρ(r)r² dr = 4πρ₀r₀ⁿ∫r²/rⁿ dr

Now you need to know for which values of n does the integral ∫1/r^n-2 dr converges. (The integral being taken from r₀ to infinity, obviously).