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Calculus Methods
Sequences are to calculus what at calculator is to a scientist. There are many ways to introduce sequences. Here we will follow a somewhat unorthodox way. Indeed, consider a scientist doing an experiment; he is collecting data, let us say, every day. So, put to be the data collected the first day, be the data collected the second day, and so on. . . . and is the data collected after n days. Clearly, we are generating a set of numbers with a very special characteristic: there is an order on the number, that is, we naturally have the first number, the second number, and so on. . . . A sequence is by definition a set of real numbers with this natural order. We will use the notation
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The notion of series is closely related to the sum of numbers. In fact, whenever one hears the word series, the first thing to come to mind is the sum of numbers. This is the basic difference between series and sequences. So series, as we will see, are here to help us add numbers. So what is the problem? Let us do a simple addition problem. Let me give 3 numbers: A, B and C. If I ask you to add them, you will take a pen and a paper or a calculator and do the following:
1. You will enter the number A, then
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