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RedAssign10[1].1 - the difference of their respective sums...

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Unit: Sequences and Series Module: Convergence and Divergence Properties of Convergent Series www.thinkwell.com [email protected] Copyright 2001, Thinkwell Corp. All Rights Reserved. 1657 –rev 06/14/2001 The terms of separate convergent series can combine to form new convergent series. Also, constant multiples can be factored into and out of convergent series. If a series converges, then the terms must be shrinking to zero. Convergent series follow many of the same rules of algebra that limits follow. For example, if you add the terms of two series together the resulting sum is equal to the sum of the two series. This works because you can break the series into two different series in the same way you can break a limit up. All of these rules parallel the limit laws . The different of the terms of two series is equal to
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Unformatted text preview: the difference of their respective sums. Finally, if you have a convergent series and you multiply its terms by some constant, the resulting series is equal to the sum of the original series times that constant. One of the conditions for a series to converge is that the terms must approach zero. Otherwise the sum of an infinite number of terms would have to be infinite. But watch out! It is a classic mistake to assume that any series whose terms approach zero must converge. Some series have terms that approach zero, but they don’t approach zero fast enough. As a consequence, the entire series diverges. So if your series converges, you know the limit of the sequence of terms is equal to zero. Is it possible to use that fact in another way?...
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