A complex function that creates a pattern that, once understood, is beautifully simple.

Difficulty: Few students have dealt with a function of this nature.

Difficulty: To be honest, I had no clue on this one. I would have to rate it difficult because the answer method seems so esoteric to this engineer. Maybe the math majors will face-palm on my obtuseness, but I'll have to risk it.

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

answer 08 and answer 34.

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