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[SPAM] [obm-l] Re: [obm-l] soma de série
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This is a multi-part message in MIME format.
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Caros amigos,
Seja n um inteiro, com n>1. O que se quer provar =E9 que
1+1/2+1/3+ . . . +1/n n=E3o =E9 inteiro.
Seja 2^a a maior pot=EAncia de 2 tal que 2^a =E9 menor do que ou igual a =
n.
Assim, 1/2^a aparece no somat=F3rio acima mas 1/2^(a+1) n=E3o =
aparece.
Observe que o m=EDnimo m=FAltiplo comum dos denominadores dos=20
termos do somat=F3rio tem a pot=EAncia 2^a como fator. Agora, no=20
numerador de cada fra=E7=E3o, j=E1 com denominador igual ao m=EDnimo
m=FAltiplo comum, temos sempre um n=FAmero par, com exce=E7=E3o do=20
termo correspondente a 1/2^a. Logo, a soma dos numeradores=20
=E9 =EDmpar o que nos leva a concluir que o somat=F3rio n=E3o =E9 um=20
n=FAmero inteiro.
Abra=E7os,
Luiz Alberto
----- Original Message -----=20
From: MauZ=20
To: obm-l@xxxxxxxxxxxxxx=20
Sent: Monday, March 10, 2008 6:13 PM
Subject: [obm-l] soma de s=E9rie
mostrar que 1+1/2+1/3+...+1/n n=E3o =E9 inteiro pra qquer N>1.
Obrigado!
-------------------------------------------------------------------------=
-----
No virus found in this incoming message.
Checked by AVG.=20
Version: 7.5.518 / Virus Database: 269.21.7/1324 - Release Date: =
10/3/2008 19:27
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charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 6.00.2900.3268" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>Caros amigos,</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Seja n um inteiro, com n>1. O que se =
quer provar=20
=E9 que</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>1+1/2+1/3+ . . . +1/n n=E3o =
=E9=20
inteiro.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Seja 2^a a maior pot=EAncia de 2 tal =
que 2^a =E9 menor=20
do que ou igual a n.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Assim, 1/2^a aparece no =
somat=F3rio acima=20
mas 1/2^(a+1) n=E3o aparece.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Observe que o m=EDnimo m=FAltiplo comum =
dos=20
denominadores dos </FONT></DIV>
<DIV><FONT face=3DArial size=3D2>termos do somat=F3rio tem a pot=EAncia =
2^a como fator.=20
Agora, no </FONT></DIV>
<DIV><FONT face=3DArial size=3D2>numerador de cada fra=E7=E3o, =
j=E1 com denominador=20
igual ao m=EDnimo</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>m=FAltiplo comum, temos sempre um =
n=FAmero par, com=20
exce=E7=E3o do </FONT></DIV>
<DIV><FONT face=3DArial size=3D2>termo correspondente a 1/2^a. Logo, a =
soma dos=20
numeradores </FONT></DIV>
<DIV><FONT face=3DArial size=3D2>=E9 =EDmpar o que nos leva a concluir =
que o somat=F3rio=20
n=E3o =E9 um </FONT></DIV>
<DIV><FONT face=3DArial size=3D2>n=FAmero inteiro.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Abra=E7os,</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Luiz Alberto</FONT></DIV>
<BLOCKQUOTE=20
style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style=3D"FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV=20
style=3D"BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>=20
<A title=3Dmauz.matematica@xxxxxxxxx=20
href=3D"mailto:mauz.matematica@xxxxxxxxx";>MauZ</A> </DIV>
<DIV style=3D"FONT: 10pt arial"><B>To:</B> <A =
title=3Dobm-l@xxxxxxxxxxxxxx=20
href=3D"mailto:obm-l@xxxxxxxxxxxxxx";>obm-l@xxxxxxxxxxxxxx</A> </DIV>
<DIV style=3D"FONT: 10pt arial"><B>Sent:</B> Monday, March 10, 2008 =
6:13=20
PM</DIV>
<DIV style=3D"FONT: 10pt arial"><B>Subject:</B> [obm-l] soma de =
s=E9rie</DIV>
<DIV><BR></DIV>mostrar que 1+1/2+1/3+...+1/n n=E3o =E9 inteiro pra =
qquer=20
N>1.<BR><BR>Obrigado!<BR>
<P>
<HR>
<P></P>No virus found in this incoming message.<BR>Checked by AVG.=20
<BR>Version: 7.5.518 / Virus Database: 269.21.7/1324 - Release Date: =
10/3/2008=20
19:27<BR></BLOCKQUOTE></BODY></HTML>
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