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I = (2/5) M (Ro^5 - Ri^5)/(Ro^3 - Ri^3)

where Ro is the distance to the very outside of the sphere and Ri is the distance to the inner thickness of the sphere if that makes sense.

I thought I could take the limit as Ri approached Ro, to yield the rotational inertia of a very thin spherical shell as I sought out for, however, I cannot evaluate the limits even if I used L'Hopital's Rule and derived the top and bottom seperately because that would not allow me to escape the cursed indeterminant form of 0/0 which results every time until the denominator goes away to zero and then i'm really in a bad situation.

I saw a website http://scienceworld.wolfram.com/physics/MomentofInertiaSphericalShell.html which reduced the (Ro^5 - Ri^5)/(Ro^3 - Ri^3) term using a series decomposition of some sort, but I have no idea what they did and it's been a while since I've meddled with Taloy Series and stuff, so any help with this or an explanation of what they did would be greatly appreciated.

THANKS! :)

Anthony