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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...

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    $\begingroup$ Write out all terms in the case $n=2$ or $n=3$. $\endgroup$
    – Kurt G.
    Oct 16, 2022 at 14:50
  • $\begingroup$ i did it for n=3. $\endgroup$
    – Syed Tallay Haidar
    Oct 16, 2022 at 15:04
  • $\begingroup$ Should be right. Probably a mistake in that "actual formula" then. $\endgroup$
    – Kurt G.
    Oct 16, 2022 at 15:09
  • $\begingroup$ It could be a difference in assumptions. For example, if you have an account earning an interest rate $i$ compounded annually, and you make a deposit of amount $G$ every year, you'll end up with a greater balance (greater by a factor of $1+i$) if you make those deposits at the beginning of each year than if you make them at the end of each year. $\endgroup$
    – David K
    Oct 16, 2022 at 15:20
  • $\begingroup$ ah i see that could be the case. $\endgroup$
    – Syed Tallay Haidar
    Oct 16, 2022 at 15:29

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