How can I compute the ratio of a geometric series given a partial sum?
Basically solve for $r$:
$$ S = \sum_{k = 0}^{n} a\,r^k = a \frac{1-r^{n+1}}{1-r}$$
given $S$, $a$ and $n$
I found this post, but it just reduces the problem to the case $a=1$, and doensn't provide a solution for this one.
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3In general: you don’t, because it involves to calculate the zeroes of a polynomial of degree $n-1$. – Michael Hoppe Jun 01 '18 at 08:58
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Thank you for your answer, this is not what I hoped for but I know I should do things differently now! – gazoh Jun 01 '18 at 09:07
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Your formula is not correct ! It should read: $\sum_{k = 0}^{n} a,r^k = a \frac{1-r^{n+1}}{1-r}$. – Fred Jun 01 '18 at 09:09
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@Fred : thanks for pointing it out, I edited the question – gazoh Jun 01 '18 at 09:11