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Article #787Re: Certain p-series...
From: Hugh Alan Grant
Date: Thu, 14 Dec 1995 00:00
Date: Thu, 14 Dec 1995 00:00
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1173 bytes
On Thu, 14 Dec 1995, Wassup star? wrote: > In article <Pine.SOL.3.91.951213220438.26087B-100000@mira.cc.umanitoba.ca> you wrote: > : 1 + 1/4 + 1/9 + 1/16 + ... + 1/(n^2)+ ... = ((pi)^2)/6, > > This looks like two geometric series in one. > (1 + 1/9 + ...)+(1/4 + 1/16 + 1/(n^2)) = ((pi)^2)/6 > > You can sum each series with the formula Sn = (a((r^n) - 1))/(r-1) > > -- rl > Ronald Low, ronl@io.org > But they aren't geometric series, because each term is not a multiple of the previous term. This can be seen if you just extend the series a little more: 1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/36 + 1/49 + 1/64 + 1/81 + ... Hugh Grant
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X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: f7972,e1973af0638960 X-Google-Attributes: gidf7972,public From: Hugh Alan Grant <umgran22@CC.UManitoba.CA> Subject: Re: Certain p-series... Date: 1995/12/14 Message-ID: <Pine.SOL.3.91.951214113513.3667A-100000@castor.cc.umanitoba.ca> X-Deja-AN: 121822694 references: <199512141344.IAA29188@twirl.io.org> content-type: TEXT/PLAIN; charset=US-ASCII organization: The University of Manitoba mime-version: 1.0 newsgroups: can.schoolnet.math.sr