What is my mistake here? I was trying to find F/G factor here

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I was trying to derive an expression for F/G factor here for homework. I have attached my working in this picture. I always end up with a (1+i) in the numerator which is not in the actual formula. What am I doing wrong here? I have been working on this all day long and have not been able to figure it out.
 I always end up with a (1+i) in the numerator which is not in the actual formula.

For n=3

Actual formula in book...