I want to simplify this fraction
$ \frac {1+a+a^2+...+a^n}{1+a^{-1}+a^{-2}+...+a^{-n}} $ where, $ a \in {\mathbb R^*} $ and $ n \in {\mathbb N^*} $
I think is some kind of formula here
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1Two geometric progressions. $\frac{\frac{a^n-1}{a-1}}{\frac{a^{-n}-1}{a^{-1}-1}}$ – user236182 Oct 10 '15 at 10:58
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Wow... I didn't think about that – Bogdan15 Oct 10 '15 at 11:01
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2You didn't really have to. Just multiply the denominator by $a^n$ and see what happens. – Ivan Neretin Oct 10 '15 at 11:10
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@IvanNeretin: Please post your comment as an answer, so that it might be accepted, and the question does not clog up the Unanswered Questions Queue. – Lucian Oct 10 '15 at 17:25
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I didn't expect it to get accepted, since the comment by user236182 pretty much does the job (albeit with an excessively powerful tool). But if you insist... – Ivan Neretin Oct 10 '15 at 18:00
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You didn't really have to use the geometric progression here (though that might help too). Just multiply the denominator by $a^n$ and see what happens.
Ivan Neretin
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