## Stony Brook University

MAT 118 Spring 2013

### Assignment 2 due in Recitation, week of February 11

*Note: assignment modified on February 7.*
- We saw in class how to understand the sum of the geometric
series
$$1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\cdots = 2$$
by marking the interval from 0 to 2 on the number line
and noting that
$$1 = 2-1$$
$$1+\frac{1}{2} = 2 - \frac{1}{2}$$
$$1+\frac{1}{2}+\frac{1}{4} = 2 - \frac{1}{4}$$
$$1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8} = 2 -\frac{1}{8}$$
etc.
Find a similar geometric explanation for
$$1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\cdots = \frac{3}{2}$$

- Problem 12 page 486
- Problem 19 page 487. The picture in the text is not very precise;
to calculate the answer,
just suppose that at each step in the process you replace each straight
segment of the curve by 9 segments, each of which is $\frac{1}{6}$
as long as the one they are replacing.
- Problem 23 page 488.
- Problem 24 page 488.
- Write an imaginative story (it can be humorous, dramatic,
whatever you like) based on geometric series and/or fractals.
This part of the assignment will be graded S/U.

Remember: Collaboration is fine, but
what you hand in *must be in your own words.* Handing in
something you copied is plagiarism and will cost you if it is
detected. Write down what you tried and how it worked.

Hand in your work at the recitation meeting (Mon, Wed or Thur)
next week.