[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

[SPAM] [obm-l] Fw: [obm-l] soma de série

SPAM: -------------------- Start SpamAssassin results ----------------------
SPAM: This mail is probably spam.  The original message has been altered
SPAM: so you can recognise or block similar unwanted mail in future.
SPAM: See http://spamassassin.org/tag/ for more details.
SPAM: 
SPAM: Content analysis details:   (5.60 hits, 5 required)
SPAM: X_MAILING_LIST     (-0.3 points) Found a X-Mailing-List header
SPAM: OUTLOOK_FW_MSG     (-0.1 points) Forwarded email (Outlook style)
SPAM: USER_AGENT_OE      (0.2 points)  X-Mailer header indicates a non-spam MUA (Outlook Express)
SPAM: SPAM_PHRASE_00_01  (0.8 points)  BODY: Spam phrases score is 00 to 01 (low)
SPAM: MAILTO_LINK        (0.2 points)  BODY: Includes a URL link to send an email
SPAM: RCVD_IN_ORBS       (2.2 points)  RBL: Received via a relay in orbs.dorkslayers.com
SPAM:                    [RBL check: found 202.146.19.200.orbs.dorkslayers.com., type: 68.178.232.99]
SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points)  RBL: Received via a relay in relays.osirusoft.com
SPAM:                    [RBL check: found 202.146.19.200.relays.osirusoft.com.]
SPAM: X_OSIRU_OPEN_RELAY (2.7 points)  RBL: DNSBL: sender is Confirmed Open Relay
SPAM: AWL                (-0.5 points) AWL: Auto-whitelist adjustment
SPAM: 
SPAM: -------------------- End of SpamAssassin results ---------------------

This is a multi-part message in MIME format.

------=_NextPart_000_001A_01C88383.FEB5C960
Content-Type: text/plain;
	charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable


----- Original Message -----=20
From: Luiz Alberto Duran Salom=E3o=20
To: obm-l@xxxxxxxxxxxxxx=20
Sent: Tuesday, March 11, 2008 10:21 AM
Subject: Re: [obm-l] soma de s=E9rie


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

------=_NextPart_000_001A_01C88383.FEB5C960
Content-Type: text/html;
	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>&nbsp;</DIV>
<DIV style=3D"FONT: 10pt arial">----- Original Message -----=20
<DIV style=3D"BACKGROUND: #e4e4e4; font-color: black"><B>From:</B> <A=20
title=3Dsalomao@xxxxxx href=3D"mailto:salomao@xxxxxx";>Luiz Alberto Duran =
Salom=E3o</A>=20
</DIV>
<DIV><B>To:</B> <A title=3Dobm-l@xxxxxxxxxxxxxx=20
href=3D"mailto:obm-l@xxxxxxxxxxxxxx";>obm-l@xxxxxxxxxxxxxx</A> </DIV>
<DIV><B>Sent:</B> Tuesday, March 11, 2008 10:21 AM</DIV>
<DIV><B>Subject:</B> Re: [obm-l] soma de s=E9rie</DIV></DIV>
<DIV><BR></DIV>
<DIV><FONT face=3DArial size=3D2>Caros amigos,</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Seja n um inteiro, com n&gt;1. O que se =
quer provar=20
=E9 que</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>1+1/2+1/3+ . . . +1/n&nbsp;&nbsp; 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&nbsp;&nbsp; aparece no =
somat=F3rio acima=20
mas 1/2^(a+1)&nbsp; 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&nbsp; 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&nbsp; 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&gt;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>

------=_NextPart_000_001A_01C88383.FEB5C960--

=========================================================================
Instruções para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=========================================================================