ch11s2 - 11.2 Series Adding the terms in an infinite...

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11.2 Series Adding the terms in an infinite sequence creates an infinite series. 12 1 nn n aaa a a = =++ + + ∑∑ LL The question is: Can we determine if the series has a sum? It’s not possible to add an infinite number of terms, but it is possible to consider partial sums to determine whether a series has a sum. It is important that you understand the difference between a sequence and a series. A sequence is a list of numbers and a series is the sum of all those numbers. Your calculator can give you a sum of a finite number of terms in a sequence. Let’s look at the series 1 2 3 n n = . The first window shows the sum of the first 10 terms in the sequence. The second window shows the sum of the first 20 terms. Do you think the series has a sum? The two sums we looked at above are partial sums. The partial sums themselves form a sequence, which may or may not have a limit. Look at the definition on page 705. 1 n n a = = s means that by taking n large enough, we can get as close as we want to the number s.
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ch11s2 - 11.2 Series Adding the terms in an infinite...

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