There is a story about a boy who later became a famous mathematician, Karl Friedrich Gauss. One day in class he was acting up and the teacher told him to add up all the integers from 1 to 100. About half a minute later, and a lot sooner than the teacher expected, young Karl gave the answer: 5050. How was he able to answer this so quickly? He saw a pattern to the integers and used that pattern to solve the problem very quickly. Here is a diagram of how he did it. Do you see it?
In this short course we will learn how to find patterns in sequences and series. We will examine the different types of sequence and focus on arithmetic and geometric sequences and series. The difference between sequences and series will be discussed as well as applications in several fields.
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