## Sample Problems from Chapter 3

**Chapter 3**: Ian's Proof: Infinity = ^{-}1
**1. Ian's problem**- Ian came back one year from Winter break with
this problem. He also brought me a copy of 'The Math Calendar' by Theoni
Pappus, where he had seen the problem.

**2. Ian proves that infinity = **^{-}1

Using what you've figured out in chapter 1, can you write as a fraction
the sum of this infinite series?

1 + a + a^{2} + a^{3} + a^{4} +
a^{5} + ... = ?

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