I hate to admit it, but I stared at this for a while, then I said to myself, "Self, this is something I'm just not going to see. There's some Geometry theorem I'm missing." So I looked at another problem and then went back to this one; still nothing. The next day, I came back to it and had the big face-palm - OMFG, it's right there.
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Difficulty: Easy if you're paying attention ...
Difficulty: Medium. Clever how the answer is possible but not obvious until you have that flash of insight ...
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2013
answer 25,
answer 26, Published 5/18.
Oh, 25 is indeed clever....
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