Example Involving Series and Partial Sums

Example Involving Series and Partial Sums - An Example of...

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An Example of the Connection Between Sequences and Series: From Section 11.2, #55 Question: Given the partial sum of our series is: find the sum of the series, and the terms in our series, a n . Solution: We have been given an the partial sums: So the first part, finding S , is the easy part: just take the limit. Finding a n isn't that bad either. Consider our partial sum: If we look at the partial sum S n 1 , we see that it stops with one term earlier, ie. without a n . So if we subtract: But we've been given a formula for S n (and thus S n 1 ): 1 1 n n S n 1 i i Sa 1 1 1 n ni i n n  1 1 1 11 0 lim lim lim 1 1 0 1 in nn n i n n aS S n n    123 1 1 .....
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This note was uploaded on 12/14/2010 for the course MATH 1za3 taught by Professor Ben during the Winter '10 term at Macalester.

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Example Involving Series and Partial Sums - An Example of...

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