Outcomes
In this lesson you will learn
- the definition of a fractal
- about the Koch snowflake
- how to use fractals to develop the formula to sum an infinite geometric series
- how to determine whether or not an infinite geometric series converges or diverges
By the end of this section students will be able to:
- demonstrate an intuitive understanding for the concept of limit
- investigate and apply the concept of infinity by examining sequences and series
- represent a series in expanded form and using sigma notation
- develop, analyze and apply algorithms to determine the sum of a series
- demonstrate an understanding of convergence and divergence
- apply convergent and divergent geometric series
- demonstrate an understanding of how to approximate the area under a curve using limits
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- the concept of similar figures
- how to find the area and perimeter simple polygons
- how to find partial sums for a series
- the concept of limit
- the difference between converging and diverging sequences
- the difference between a sequence and a series
- how to express a series using sigma notation
- the formula used to sum a finite geometric series
- how to work with radicals (for question #28)
- the concept of probability (for question #35)