Weird expressions and the Sum of an Infinite Series ... yum.

Difficulty: moderately difficult. Students have trouble if you ask for the value of an expression rather than for a value of x. How does that second expression relate to the first?

Difficulty: Sum of a series. But what's the ratio?

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 15 and answer 27.

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