MATH 231 Lecture Notes - Lecture 15: Direct Comparison Test
13 Mar 2015
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Bn be series with positive terms converges, and an < bn for all large values of n, then . An also diverges, and an > bn for all large values of n, then . Compare a given series to a known series. Geometric series: converges if p > 1, diverges if p 1. Arn 1 converges if r <1 , and diverges otherwise. An is the dominating term in the denominator so we can assign . Bn we find that it can be simplified into a p series. In this case, p = 2, and so we know that . 2. is the dominating term in the numerator so we can assign . Because it is a harmonic series, we know that original series ( . The subtraction of terms in the denominator makes it difficult to choose a larger series for. Bn are still series with positive terms, let.
