Article View: sci.math.num-analysis
Article #828Re: Does this product converge ???
From: Dave Dodson
Date: Tue, 22 Dec 1992 19:25
Date: Tue, 22 Dec 1992 19:25
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1748 bytes
In article <1992Dec22.165148.20421@draper.com> storch@draper.com (Joel Storch) writes: > >To prove that Product(k=3,infinity, Cos(Pi/k)) converges, first rewrite it as >Product(k=3,infinity,1-2 (Sin(Pi/2k))^2). This product will converge >(absolutely) if the infinite series Sum(k=3,infinity,(Sin(Pi/2k))^2) >converges. The Ratio Test fails here but Raabe's test shows that the series >converges. > >One source of theorems on convergence of infinite Products is Whittaker & >Watson, "A course in Modern Analysis" Even simpler: The sequence of partial products is non-negative and monotone- decreasing. Therefore it has a greatest lower bound, which must be the limit. ---------------------------------------------------------------------- Dave Dodson dodson@convex.COM Convex Computer Corporation Richardson, Texas (214) 497-4234
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From: Dave Dodson <dodson@convex.COM>
Subject: Re: Does this product converge ???
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Date: Tue, 22 Dec 1992 19:25:35 GMT
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Organization: Engineering, CONVEX Computer Corp., Richardson, Tx., USA
Keywords: Infinite products, convergence
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