Calc Formula Sheet - n . If the limn anbn = L then, 1. If L...

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Divergence test If the →∞ limn an 0 then the series a n diverges. If →∞ = limn an 0 then the divergence test fails Geometric Series Test The series = ∞ n 0 rn converges if |r|<1. Diverges otherwise. Convergence of Geometric Series To determine what each geometric series converges to use the following equations: If |r| < 1, then the series converges: = ∞ n 0 crn = - 11 r or = ∞ n m crn = - crm1 r If |r| > 1, then the series diverges but the partial sum is: = = ( - + ) - n mNcrn c 1 rN 1 1 r Integral Test For the series, = ∞ n 0 an , an 0 for all n then define a function, f(x), such that f(n) = an and if m fxdx converges then the series a n converges as well P-Test The sum = ∞ n 1 1np converges if p > 1 and diverges if p ≤ 1 Comparison Test 0 ≤ a n ≤b n If = ∞ n 0 bn converges then = ∞ n 0 an also converges If = ∞ n 0 an diverges then = ∞ n 0 bn also diverges. Limit Comparison Test There is a series = ∞ n 0 an . Find the simplified version of a n , call that series b
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Unformatted text preview: n . If the limn anbn = L then, 1. If L = 0 and = n 0 bn converges then = n 0 an converges 2. If L &gt; 0 then = n 0 an iff = n 0 bn converges Absolute Convergence an is called absolutely convergent if an converges Conditional Convergence an is called conditionally convergent if an converges and an diverges Leibniz Alternating Series Test Iff : i) a n &gt; a n+1 and ii) = limn an 0 (a n converges to 0) Then the following alternating series is said to conditionally converge: = n 0 Qan , where Q is (-1) n , (-1) n+1 , (-1) n-1 , etc. Root Test = L limn nan i) If L &lt; 1 then an converges absolutely ii) If L &gt; 1 then an diverges iii) If L = 1 then the test fails and is inconclusive Ratio Test = + limn an 1an iv) If &lt; 1 then an converges absolutely v) If &gt; 1 then an diverges vi) If = 1 then the test fails and is inconclusive...
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This note was uploaded on 10/12/2009 for the course MATH calculus 3 taught by Professor Ningzhong during the Spring '08 term at University of Cincinnati.

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Calc Formula Sheet - n . If the limn anbn = L then, 1. If L...

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