Re: Does this product converge ???

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#824

From: Joel Storch
Date: Tue, 22 Dec 1992 16:51

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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"

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From: storch@draper.com (Joel Storch)
Subject: Re: Does this product converge ???
Message-ID: <1992Dec22.165148.20421@draper.com>
Keywords: Infinite products, convergence
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Date: Tue, 22 Dec 1992 16:51:48 GMT
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