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Published byEvelyn Jenkins Modified over 8 years ago
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In this section, we will begin investigating infinite sums. We will look at some general ideas, but then focus on one specific type of series.
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For example:
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1. Which series sum to a finite number? 2. How do we find/approximate such sums? 3. Which series blow up to ? 4. Which series diverge without blowing up to ?
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Let be the sequence of partial sums. The series converges if the sequence converges. The series diverges if the sequence diverges.
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Show that the given converges by finding an algebraic formula for.
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Finding an algebraic formula for is not, in general, easy to do. Thus, determining the convergence/divergence of a series is not, in general, easy to do either. For a certain, very special, type of series, these questions are significantly easier.
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If, the geometric series converges to. If the sum does not start at k = 0, then the limiting sum is. If a ≠ 0 and, the series diverges.
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Determine whether the given series converges or diverges. If it converges, give the sum. If it diverges, find N so that S N ≥ 1000.
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If, then diverges. NOTE: If, we can say nothing about the convergence or divergence of.
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diverges because. diverges even though.
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