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8.3 Notes - 1 1 n n Example 1 2 1 n n p-series and Harmonic...

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Section 8.3, The integral test p-series and harmonic series In this section we restrict our attention to Positive term series and convergence tests Theorem 9 The Integral Test If f is positive, continuous, and decreasing for 1 x and ) ( n f a n , then 1 n n a and 1 ) ( dx x f either both converge or both diverge.(Note: this does not say that the series and the integral converge to the same sum) Example: Determine the convergence or divergence of the series: Example:
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Unformatted text preview: 1 1 n n Example: 1 2 1 n n p-series and Harmonic Series A p-series is one of the form ... 3 1 2 1 1 1 1 1 p p p n p n When p=1 , the series becomes ... 3 1 2 1 1 1 1 1 p n n and is called the Harmonic Series As you saw in the above examples we can use the integral test to determine the p-series test which tells us that a p-series converges if p>1 and diverges if 1 p (therefore the harmonic series diverges) Examples:...
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