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Homework Statement
This isn't strictly a homework problem, but I didn't know where else to post this. I can't get the same derivation as my lecturer for the Doppler effect of light  which is shown in the attached file. If you cannot open this, I rewrote it further down.
Homework Equations
The Attempt at a Solution
For the part in the red box, I thought one would do this via Taylor expansion, thus I expected the ##\frac{u}{c}## to be squared, i.e f_{r} = f_{s}##(1 \pm \frac{1}{2}\frac{u}{c}^2)(1 \pm \frac{1}{2}\frac{u}{c}^2)##. I can't see why this wouldn't be the case. Could someone please tell me why I'm wrong?
(In case you cannot open the file, my lecture notes say f_{r} = f_{s}##(1 \pm \frac{u}{c})^\frac{1}{2} (1 \pm \frac{u}{c})^\frac{1}{2}##=##(1 \pm \frac{1}{2}\frac{u}{c})(1 \pm \frac{1}{2}\frac{u}{c})##)
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