I am proving a theorem and found here in the following geometric series $a^{n-1}+...+a^2k^{n-3}+ak^{n-2}+k^{n-1}$ what would be the sum of this series.
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Have you seen the expansion of $(a^n-k^n)$ before? – rtybase Oct 10 '17 at 17:05
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Like this one for instance https://math.stackexchange.com/questions/309692/how-to-factor-an-bn – rtybase Oct 10 '17 at 17:13
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I know the formula of sum of finite geometric series, which is $S_n=\dfrac{(a^n)(1-r^{n-1})}{1-r}$ – Harjeet Singh Oct 10 '17 at 17:14
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Yep, so try to use it for $r=\frac{k}{a}$ – rtybase Oct 10 '17 at 17:17
