[mugsy777]

you should be able to proof that the reduced mass of deutereum is approximately:
            me[1 - 0.5(me/mp) + 0.25(me/mp)^2 -...]

does anyone have any insight?

[Yggdrasil]

This is a pretty tricky question.  Here's one hint: you'll need to make a Taylor expansion of the function 1/(1+x) where x is small.

Other than that hint, I'd say to start with a formula for the reduced mass of a two body system.

[mugsy777]

those are exactly the two hints that I managed to figure out. I cannot get much farther due to my lack of mathematical insight when it comes to proofs 

[mugsy777]

I know that I need to apply the formula (1/1+x) * sum from n=0 to n=infinity (-1)^n*X^n
to the fraction (2mpme)/(2mp+me) but I am still not seeing the proof. I am sorry if I sound demented, or if I am wrong, I have been studying the entire weekend for an exam!

[Yggdrasil]

You are very close to getting the right derivation.  Now, can you get 2mpme/(2mp+me) to look like 1/(1+x)?  (hint: factor out me first).  If so, what is x?  If you plug that into your formula for the Taylor expansion, you should get the right result.

[mugsy777]