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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 S a 1 1 1 n n i i n S a n 1 1 1 1 1 0 lim lim lim 1 1 1 1 0 1 i n n n n i n n a S S n n    1 2 3 1 1 ..... n n

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

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