Calculus (infinite series) - Gravitational Potential Energy Problem

[sonikbliss]

Homework Statement

[PLAIN]http://img818.imageshack.us/img818/817/potentialenergy.jpg

Homework Equations

Given above.

The Attempt at a Solution

I've never had physics in my life and am completely baffled by this problem. I'm only in calculus 3 and am just learning infinite series so I am supposed to be able to understand this on some level but I can't even figure out how to start. I'm not asking anybody to just give me the answer but if anyone can help me get started in the right direction I'd greatly appreciate it. I want to be able to comprehend this stuff but I don't feel like my calculus skills are there yet after only a few weeks. Thanks to anyone gracious enough to help!

 

[AKG]

You don't need to know any physics to do this problem, just follow the hint. Figure out a way to express U as a function of h/R (and a bunch of constants), and then write out the power series expansion. This infinite power series is supposed to approximately equal -mgR + mgh.

 

[echolalia127]

So are you saying to solve U for both h and R, divide the two, then solve for U?

 

[Zdua7]

Try multiplying both the top and bottom of the equation by R so that you can factor another R out of the bottom, leaving you with a (-GmMR)/[R^2(1+h/R)]. Then use your GM/R^2 = 9.8 to end up with (-9.8mR)/(1-(-h/R)). From here, it's a simple power series of type a/(1-r).