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Sect. 9-D Comparison Tests . The Direct comparison Test . If 0 < a n < b n for all n and positive terms, then: If the larger series converges, then the smaller series must also converge. If the smaller series diverges then the larger series must also diverge. The Direct comparison Test .
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The Direct comparison Test If 0 < an < bnfor all n and positive terms, then: If the larger series converges, then the smaller series must also converge. If the smaller series diverges then the larger series must also diverge
The Direct comparison Test Given a series Compare with a similar Geometric or p- Series When choosing a series for comparison you can disregard all but the highest power in the numerator and denominator When choosing an appropriate p-series, you must choose one with the same nth term
The Limit comparison Test If an >0, and bn> 0 for all n , then: Where L is finite and positive, then both converge or they both diverge Works well when comparing a messy algebraic series to a p-series or geometric series
Home Work Page 630 # 3,4,5,8,9,10,11,14,15,17,19,21,29-35 all