A solution I'm looking at employs this formula to find the sum of a finite series, but I haven't been able to find any information on this formula online or in my textbooks. Where does it come from, and what situations does it apply to? (It doesn't seem to be a reorganization of the formula for finite geometric sums...)
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What do you mean when you say "the summation formula $(c^n-1)/(c-1)$"? Do you mean the identity $\sum_{k = 0}^{n-1} c^k = \frac{c^n-1}{c-1}$? – Arthur Nov 27 '19 at 14:57
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3It is a geometric sum. It comes up whenever you ehm, sum geometries. – mathreadler Nov 27 '19 at 14:58
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It is just the sum of a finite geometric series (you seem to know that). It's useful in very many places. – Ethan Bolker Nov 27 '19 at 14:59
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Does this or this help ? – Arnaud D. Nov 27 '19 at 15:01
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@EthanBolker Oh...I thought the sum of a finite geometric series was $\frac{a_0(1-r^n)}{1-r}$? – James Ronald Nov 27 '19 at 15:02
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Suppose $a_0=1$? – saulspatz Nov 27 '19 at 15:02
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@JamesRonald yes it is special case $a_0 = 1$ – mathreadler Nov 27 '19 at 15:03
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It comes from the high-school formula: $$a^n-b^n=(a-b)(a^{n-1}+a^{n-2}b+\dots+ab^{n-2}+b^{n-1})$$ with $a=1$.
Bernard
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