MATH 1552 : Math 1552 Summary Of Tests For Convergence For Test 3
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The integral test: suppose f is a continuous, positive, decreasing function on. =1n words, na is convergent if and only if the improper integral . )( dx is convergent, then is divergent, then . The comparison test: suppose that na and nb are series with positive terms. If nb is divergent and n a a n b n b n for all n, then na is also convergent. for all n, then na is also divergent. (i) (ii) The limit comparison test: suppose that na and nb are series with positive terms. If lim n a n b n c where c is a finite number and c > 0, then either both series converge or both diverge. The alternating series test: if the alternating series . +1 b b n n lim = b. 1 or if lim n a 1 n a n. If a lim 1 =+ n n a n.
