[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
[SPAM] [obm-l] RES: [obm-l] [obm-l] Questão de indução matemática
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: (5.30 hits, 5 required)
SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header
SPAM: REFERENCES (-0.5 points) Has a valid-looking References header
SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header
SPAM: NOSPAM_INC (-0.2 points) Where are you working at?
SPAM: INVALID_MSGID (0.0 points) Message-Id is not valid, according to RFC 2822
SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low)
SPAM: HTML_50_70 (0.3 points) BODY: Message is 50-70% HTML tags
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 197.4.63.201.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 197.4.63.201.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 ---------------------
Esta é uma mensagem em várias partes no formato MIME.
------=_NextPart_000_001F_01C87E0D.2466F160
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
Ol=E1 Marcelo Salhab,
=20
Muito grato.
=20
Sds
=20
Rubens Kamimura=20
Assistente T=E9cnico III - CREA/SP 5062246285
CESP - Companhia Energ=E9tica de S=E3o Paulo
OMPTD - Capacita=E7=E3o e Desenvolvimento
Caixa Postal, 58 - CEP 15385-000
Ilha Solteira/SP - Brasil
Tel. +55-18-3704-4240 ramal 136/137
Tel./Fax +55-18-3704-6800
www.cesp.com.br
email: rubens.kamimura@xxxxxxxxxxx=20
Mens In Corpore Tantun Molen Regit
UNYK : 132 XOU
P Antes de imprimir pense em sua responsabilidade e compromisso com o =
MEIO
AMBIENTE.
=20
=20
=20
De: owner-obm-l@xxxxxxxxxxxxxx [mailto:owner-obm-l@xxxxxxxxxxxxxx] Em =
nome
de Marcelo Salhab Brogliato
Enviada em: ter=E7a-feira, 4 de mar=E7o de 2008 14:29
Para: obm-l@xxxxxxxxxxxxxx
Assunto: Re: [obm-l] [obm-l] Quest=E3o de indu=E7=E3o matem=E1tica
=20
Ol=E1 Rubens,
Essas demonstra=E7=F5es seguem todas a mesma id=E9ia...
vou fazer apenas o 2.1
veja que para n=3D1 =E9 v=E1lido
vamos supor valido para K e vamos mostrar que vale para K+1.
isto =E9:
Hip=F3tese: 1^2 + 2^2 + ... + k^2 =3D [k(k+1)(2k+1)]/6
Tese: 1^2 + 2^2 + ... + k^2 + (k+1)^2 =3D (k+1)(k+2)(2k+3)/6
Demo:
Sabemos que: 1^2 + 2^2 + .. + k^2 =3D k(k+1)(2k+1)/6
somando (k+1)^2 em ambos os lados, temos:
1^2 + 2^2 + ... + k^2 + (k+1)^2 =3D k(k+1)(2k+1)/6 + (k+1)^2
vamos apenas fatorar o lado direito, e mostrar que ele =E9 igual a
(k+1)(k+2)(2k+3)/6 =3D (k+1)(2k^2 + 7k + 6)/6
k(k+1)(2k+1)/6 + (k+1)^2 =3D (k+1)[ k(2k+1)/6 + (k+1) ] =3D (k+1)[ 2k^2 =
+ k + 6k
+ 6 ]/6 =3D (k+1)(2k^2 + 7k + 6)/6
logo, est=E1 provado por indu=E7=E3o.
abra=E7os,
Salhab
2008/3/3 Rubens Kamimura <rubens.kamimura@xxxxxxxxxxx>:
Ol=E1 turma da LISTA!!!
Algu=E9m desta LISTA, se habilitariam em me elucidar tal quest=E3o?
1. Sabendo, por defini=E7=E3o, que: a^0=3D1 e a^1=3Da, como poderemos =
provar por
indu=E7=E3o matem=E1tica sobre n, que a^m.a^n =3D a^(m+n), para qualquer =
m,n
pertencente ao conjunto dos n=FAmeros naturais?
2. Como podemos provar por indu=E7=E3o matem=E1tica:
2.1. 1^2+ 2^2+...+n^2 =3D [n(n+1)(2n+1)]/6, (n maior igual 1);
2.2. 1^3+ 2^3+...+n^3 =3D (1+2+...+n)^2, (n maior igual 1);
2.3. 1.2+2.3+...+n(n+1) =3D [n(n+1)(n+2)]/3, (n maior igual 1);
Abra=E7os
leigo e ne=F3fito...
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
<http://www.mat.puc-rio.br/%7Eobmlistas/obm-l.html>=20
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
--=20
Esta mensagem foi verificada pelo sistema de antiv=EDrus e=20
acredita-se estar livre de perigo.=20
------=_NextPart_000_001F_01C87E0D.2466F160
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
<META HTTP-EQUIV=3D"Content-Type" CONTENT=3D"text/html; =
charset=3Diso-8859-1">
<html xmlns:v=3D"urn:schemas-microsoft-com:vml" =
xmlns:o=3D"urn:schemas-microsoft-com:office:office" =
xmlns:w=3D"urn:schemas-microsoft-com:office:word" =
xmlns:x=3D"urn:schemas-microsoft-com:office:excel" =
xmlns:m=3D"http://schemas.microsoft.com/office/2004/12/omml"; =
xmlns=3D"http://www.w3.org/TR/REC-html40";>
<head>
<meta name=3DGenerator content=3D"Microsoft Word 12 (filtered medium)">
<style>
<!--
/* Font Definitions */
@font-face
{font-family:"MS Mincho";
panose-1:2 2 6 9 4 2 5 8 3 4;}
@font-face
{font-family:"MS Mincho";
panose-1:2 2 6 9 4 2 5 8 3 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:Tahoma;
panose-1:2 11 6 4 3 5 4 4 2 4;}
@font-face
{font-family:"\@MS Mincho";
panose-1:2 2 6 9 4 2 5 8 3 4;}
@font-face
{font-family:Verdana;
panose-1:2 11 6 4 3 5 4 4 2 4;}
@font-face
{font-family:Webdings;
panose-1:5 3 1 2 1 5 9 6 7 3;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman","serif";}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
span.EstiloDeEmail17
{mso-style-type:personal-reply;
font-family:"Calibri","sans-serif";
color:#1F497D;}
.MsoChpDefault
{mso-style-type:export-only;}
@page Section1
{size:612.0pt 792.0pt;
margin:70.85pt 3.0cm 70.85pt 3.0cm;}
div.Section1
{page:Section1;}
-->
</style>
<!--[if gte mso 9]><xml>
<o:shapedefaults v:ext=3D"edit" spidmax=3D"1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext=3D"edit">
<o:idmap v:ext=3D"edit" data=3D"1" />
</o:shapelayout></xml><![endif]-->
</head>
<body lang=3DPT-BR link=3Dblue vlink=3Dpurple>
<div class=3DSection1>
<p class=3DMsoNormal><span =
style=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Ol=E1 Marcelo Salhab,<o:p></o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Muito grato.<o:p></o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Sds<o:p></o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=3DMsoNormal><b><span =
style=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Rubens Kamimura <o:p></o:p></span></b></p>
<p class=3DMsoNormal><span =
style=3D'font-size:8.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Assistente T=E9cnico III - CREA/SP =
5062246285<o:p></o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:8.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>CESP - Companhia Energ=E9tica de S=E3o =
Paulo<o:p></o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:8.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>OMPTD - Capacita=E7=E3o e =
Desenvolvimento<o:p></o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:8.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Caixa Postal, 58 - CEP 15385-000<o:p></o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:8.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Ilha Solteira/SP - Brasil<o:p></o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:8.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Tel. +55-18-3704-4240 ramal 136/137<o:p></o:p></span></p>
<p class=3DMsoNormal><span lang=3DEN-US =
style=3D'font-size:8.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Tel./Fax +55-18-3704-6800<o:p></o:p></span></p>
<p class=3DMsoNormal><span lang=3DEN-US =
style=3D'font-size:8.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><a =
href=3D"http://www.cesp.com.br";>www.cesp.com.br</a><o:p></o:p></span></p>=
<p class=3DMsoNormal><span lang=3DEN-US =
style=3D'font-size:8.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>email: <a =
href=3D"mailto:rubens.kamimura@xxxxxxxxxxx";>rubens.kamimura@xxxxxxxxxxx</=
a>
<o:p></o:p></span></p>
<p class=3DMsoNormal><b><span lang=3DEN-US =
style=3D'font-size:8.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Mens In Corpore Tantun Molen =
Regit<o:p></o:p></span></b></p>
<p class=3DMsoNormal =
style=3D'text-align:justify;text-justify:inter-ideograph;
line-height:10.5pt'><b><span =
style=3D'font-size:8.0pt;font-family:"Calibri","sans-serif";
color:#003366'>UNYK : 132 XOU<o:p></o:p></span></b></p>
<p class=3DMsoNormal><b><span =
style=3D'font-size:13.5pt;font-family:Webdings;
color:green'>P</span></b><b><span =
style=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'> </span></b><b><span =
style=3D'font-size:7.5pt;font-family:"Verdana","sans-serif";
color:green'>Antes de imprimir pense em sua responsabilidade e =
compromisso com
o MEIO AMBIENTE.</span></b><span =
style=3D'font-family:"Calibri","sans-serif";
color:#1F497D'><o:p></o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<div style=3D'border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt =
0cm 0cm 0cm'>
<p class=3DMsoNormal><b><span =
style=3D'font-size:10.0pt;font-family:"Tahoma","sans-serif"'>De:</span></=
b><span
style=3D'font-size:10.0pt;font-family:"Tahoma","sans-serif"'>
owner-obm-l@xxxxxxxxxxxxxx [mailto:owner-obm-l@xxxxxxxxxxxxxx] <b>Em =
nome de </b>Marcelo
Salhab Brogliato<br>
<b>Enviada em:</b> ter=E7a-feira, 4 de mar=E7o de 2008 14:29<br>
<b>Para:</b> obm-l@xxxxxxxxxxxxxx<br>
<b>Assunto:</b> Re: [obm-l] [obm-l] Quest=E3o de indu=E7=E3o =
matem=E1tica<o:p></o:p></span></p>
</div>
<p class=3DMsoNormal><o:p> </o:p></p>
<p class=3DMsoNormal style=3D'margin-bottom:12.0pt'>Ol=E1 Rubens,<br>
<br>
Essas demonstra=E7=F5es seguem todas a mesma id=E9ia...<br>
vou fazer apenas o 2.1<br>
veja que para n=3D1 =E9 v=E1lido<br>
<br>
vamos supor valido para K e vamos mostrar que vale para K+1.<br>
isto =E9:<br>
Hip=F3tese: 1^2 + 2^2 + ... + k^2 =3D [k(k+1)(2k+1)]/6<br>
Tese: 1^2 + 2^2 + ... + k^2 + (k+1)^2 =3D (k+1)(k+2)(2k+3)/6<br>
<br>
Demo:<br>
Sabemos que: 1^2 + 2^2 + .. + k^2 =3D k(k+1)(2k+1)/6<br>
somando (k+1)^2 em ambos os lados, temos:<br>
1^2 + 2^2 + ... + k^2 + (k+1)^2 =3D k(k+1)(2k+1)/6 + (k+1)^2<br>
<br>
vamos apenas fatorar o lado direito, e mostrar que ele =E9 igual a
(k+1)(k+2)(2k+3)/6 =3D (k+1)(2k^2 + 7k + 6)/6<br>
k(k+1)(2k+1)/6 + (k+1)^2 =3D (k+1)[ k(2k+1)/6 + (k+1) ] =3D (k+1)[ 2k^2 =
+ k + 6k +
6 ]/6 =3D (k+1)(2k^2 + 7k + 6)/6<br>
<br>
logo, est=E1 provado por indu=E7=E3o.<br>
<br>
abra=E7os,<br>
Salhab<br>
<br>
<br>
<o:p></o:p></p>
<div>
<p class=3DMsoNormal>2008/3/3 Rubens Kamimura <<a
href=3D"mailto:rubens.kamimura@xxxxxxxxxxx";>rubens.kamimura@xxxxxxxxxxx</=
a>>:<o:p></o:p></p>
<p class=3DMsoNormal>Ol=E1 turma da LISTA!!!<br>
<br>
Algu=E9m desta LISTA, se habilitariam em me elucidar tal quest=E3o?<br>
<br>
1. Sabendo, por defini=E7=E3o, que: a^0=3D1 e a^1=3Da, como poderemos =
provar por<br>
indu=E7=E3o matem=E1tica sobre n, que a^m.a^n =3D a^(m+n), para qualquer =
m,n<br>
pertencente ao conjunto dos n=FAmeros naturais?<br>
<br>
2. Como podemos provar por indu=E7=E3o matem=E1tica:<br>
2.1. 1^2+ 2^2+...+n^2 =3D [n(n+1)(2n+1)]/6, (n maior igual 1);<br>
2.2. 1^3+ 2^3+...+n^3 =3D (1+2+...+n)^2, (n maior igual 1);<br>
2.3. 1.2+2.3+...+n(n+1) =3D [n(n+1)(n+2)]/3, (n maior igual 1);<br>
<br>
Abra=E7os<br>
<br>
leigo e ne=F3fito...<br>
<br>
<br>
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D<br>=
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em<br>
<a href=3D"http://www.mat.puc-rio.br/%7Eobmlistas/obm-l.html"; =
target=3D"_blank">http://www.mat.puc-rio.br/~obmlistas/obm-l.html</a><br>=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D<o:p=
></o:p></p>
</div>
<p class=3DMsoNormal><br>
<br>
-- <br>
Esta mensagem foi verificada pelo sistema de antiv=EDrus e <br>
acredita-se estar livre de perigo. <o:p></o:p></p>
</div>
</body>
</html>
------=_NextPart_000_001F_01C87E0D.2466F160--
=========================================================================
Instruções para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=========================================================================