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Give (a) the first four terms of the sequence for which $a_{n}$ is given and $(b)$ the first four terms of the infinite series associated with the sequence.$$a_{n}=\frac{1}{n}+\frac{1}{n+1}, \quad n=1,2,3, \dots$$

Calculus 2 / BC

Chapter 30

Expansion of Functions in Series

Section 1

Infinite Series

Series

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we want to find the first four terms of the sequence in series for which is given for each term of the sequence is A. N equals one over N plus one over N plus one. And and is given as +123 and so forth. Therefore the first four terms of sequences series are found for a one, A two, A three and a four. So in order to first find the sequence terms, we need to note that defined each sequence terms. We simply plug in the corresponding value, and for a one we have 1/1 plus 1/1 +182 is defined similarly and so on. So we first have a one is 1/1 plus 1/1 plus one. As I mentioned, three halfs A two is one half plus one, third equals +56 Then we have a three equals one third +147 12 and +84 is 1/4 plus 1/5 equals 9 20. Now we can like the series. Remember that the series is that some of our a. M. For the first four terms of our series is given as the sum of our A one through a four or three half plus five, six plus 7, 12 plus 9/20.

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