I am stuck on this proof and I need assistance please. Not sure if it's the right start but here is what I've done so far: I let $x=2^{n-1}$ and $2x=2^x$ that will change the expression to $2^{2x}+2^x+1$ than $y=2^x$ so the expression will be $y^2+y+1$ which is equal to $\frac{y^3-1}{y-1}$. I am stuck there and don't know how to continue further or if this is the right approach. Thank you for your assistance.
Oli.