Stage: 4 Challenge Level: 
Hint for part 2
You might need to ask your teacher to explain to you how to sum a Geometric Progression.
Alternatively there are some ideas on the NRICH site- but this diagram might give you some ideas:
Pythagoras' theorem. Squares. Interactivities. Circles. Summation of series. Mathematical reasoning & proof. Generalising. Limits. Geometric sequence. Long problems.
Published March 2003,April 2003.
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NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk