2004 #06 and 36

How well do yours remember their geometry rules?

Difficulty: Similar triangles.  Simple.

Difficulty: It's the obligatory infinite series, but what's the ratio? That's what will trip them up.

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 2004

answer 06, answer 36.