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I'll be happy if you could help me prove this argument with algebraic tools:

$${N\choose 0}a^N+{N\choose 1}a^{N-2}+{N\choose 2}a^{N-4}+{N\choose 3}a^{N-6}+\dots = \frac{a^2+1}{a}$$

Thanks, Don

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    oops, editing is out of sync. Sorry @Zev2011-10-11
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    Very out of sync, I hope I didn't break too much editing. $\LaTeX>>$ image.2011-10-11
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    Yeah, it's looking good now, sorry about the mixup. (Didn't there use to be notifications when an edit was made to a post you were editing?)2011-10-11
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    This question has gone through 6 edits within 8 minutes. Perhaps we should let the post settle down a bit :)2011-10-11
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    I don't think the formula is correct. I get $(a+1/a)^n$ for the binomial sum.2011-10-11
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    That's really an equality, rather than an "argument".2011-10-11

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