series-strategies

series-strategies - Instructor: Dr. Farzana Chaudhry MATH...

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Instructor: Dr. Farzana Chaudhry MATH 1042 -Calculus II CH 8. Strategy for Series . Here is a quick listing of all the test that we’ve got. 1. Divergence Test: If lim n →∞ a n ± = 0 then a n will diverge. 2. Integral Test: Suppose that f ( x ) is a positive, decreasing function on the interval [ k, ) and that f ( n ) = a n then, i. If R k f ( x ) dx is convergent so is X n = k a n . ii. If R k f ( x ) dx is divergent so is X n = k a n . 3. Comparison Test: Suppose that we have two series a n and b n with a n 0 and b 0 for all n and a n b n for all n . Then, i. If b n is convergent then so is a n . ii. If b n is divergent then so is a n . 4. Limit Comparison Test: Suppose that we have two series a n and b n with a n 0 and b n ) for all n . Suppose that lim n →∞ a n b n = L i. If L is positive (i.e. L > 0 ) and is finite (i.e. L < ) then either both series converge or both series diverge. ii.
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This note was uploaded on 04/18/2008 for the course MATH 1042 taught by Professor Dr.z during the Spring '08 term at Temple.

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series-strategies - Instructor: Dr. Farzana Chaudhry MATH...

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