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I'm using a book for my AS Level maths which says that:

"The general rule for the sum of a geometric series is $$S_n = a\frac{r^n-1}{r-1}$$ or $$S_n= a\frac{1-r^n}{1-r}$$ "

Why are there two formulas and when do I use each?

Thanks so much, I'm really confused!

Sami x

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  • $\begingroup$ Thanks Parisa- I'm new at using the site! :) $\endgroup$
    – Sami
    Apr 26, 2015 at 16:39
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    $\begingroup$ They are the same ; multiply numerator and denominator by $-1$ to pass from one to the other $\endgroup$
    – marwalix
    Apr 26, 2015 at 16:39
  • $\begingroup$ The general rule only applies if $r \neq 1$. If $r = 1$, then $S_n = na$. $\endgroup$
    – N. F. Taussig
    Apr 26, 2015 at 20:14

1 Answer 1

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They are the same formula, the only difference is that you take out a $-1$ at the numerator and at the denominator so they turn into $1$ which is obv not written. Let me show you:

$S_n=\frac {a(r^n-1)} {r-1}=\frac {(-1)a(1-r^n)} {r-1}=\frac {(-1)a(1-r^n)} {(-1)(1-r)}=\frac {a(1-r^n)} {(1-r)}$

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  • $\begingroup$ Sorry if i'm being really dim- I'm trying to teach myself and can't always manage it! $\endgroup$
    – Sami
    Apr 26, 2015 at 16:42
  • $\begingroup$ Vote mine as answer if you find it complete, btw is always a pleasure to help. $\endgroup$
    – AlienRem
    Apr 26, 2015 at 16:58

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