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[SPAM] RE: [obm-l] trigonometria 2



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Sauda,c~oes,=20
=20
Oi Pedro,=20
=20
Mais uma vez recorri ao prof. Rousseau e ele=20
me mandou a solu=E7=E3o.=20
=20
Bem, ele se desculpou por mandar uma solu=E7=E3o parcial=20
pois ($\ast$) foi considerado um resultado conhecido.=20
Uma soma parecida usando \csc^2 no lugar de=20
\sec^2 apareceu na AMM de 1967.=20
=20
Foi ele tamb=E9m que mandou a soma resolvida pelo=20
Ralph.=20
=20
Fica ent=E3o o problema de mostrar ($\ast$).=20
=3D=3D=3D
C=F3pia do c=F3digo LaTeX=20
=20
This is easily proved with the aid of\begin{equation}\sum_{k=3D0}^{2n-1} \s=
ec^2 \left( \frac{\pi(2k+1)}{4n} \right) =3D4n^2. \tag{$\ast$}\end{equation=
}Using ($\ast$) with $n =3D 45$, straightforward calculation gives\begin{al=
ign*}\sum_{k=3D0}^{89} \tan^2 \left( \frac{\pi(2k+1)}{180} \right) & =3D\fr=
ac{1}{2} \sum_{k=3D0}^{89} \left\{  \sec^2 \left(\frac{\pi(2k+1)}{180} \rig=
ht)  - 1 \right\} \\[.1in]& =3D \frac{1}{2} (90^2 - 90) =3D 4005.\end{align=
*}=3D=3D=3D []'s=20
Lu=EDs=20


From: npc1972@xxxxxxxxxxx: obm-l@xxxxxxxxxxxxxxxxxxxxx: [obm-l] trigonometr=
ia 2Date: Thu, 1 Nov 2001 03:25:29 -0200




Feras da lista como fa=E7o issa?
=20
Prove que :=20
_________________________________________________________________
Confira v=EDdeos com not=EDcias do NY Times, gols direto do Lance, videocas=
setadas e muito mais no MSN Video!
http://video.msn.com/?mkt=3Dpt-br=

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<style>
.hmmessage P
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margin:0px;
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<body class=3D'hmmessage'>
Sauda,c~oes, <BR>
&nbsp;<BR>
Oi Pedro, <BR>
&nbsp;<BR>
Mais uma vez recorri ao prof. Rousseau e ele <BR>
me mandou a solu=E7=E3o. <BR>
&nbsp;<BR>
Bem, ele se desculpou por mandar uma&nbsp;solu=E7=E3o parcial <BR>
pois ($\ast$) foi&nbsp;considerado um resultado conhecido. <BR>
Uma soma parecida usando \csc^2 no lugar de <BR>
\sec^2 apareceu na AMM de 1967. <BR>
&nbsp;<BR>
Foi ele tamb=E9m que mandou a soma resolvida pelo <BR>
Ralph. <BR>
&nbsp;<BR>
Fica ent=E3o o problema de mostrar ($\ast$). <BR>
<BR>=3D=3D=3D<BR>
C=F3pia do c=F3digo LaTeX <BR>
&nbsp;<BR>
This is easily proved with the aid of<BR>\begin{equation}<BR>\sum_{k=3D0}^{=
2n-1} \sec^2 \left( \frac{\pi(2k+1)}{4n} \right) =3D<BR>4n^2. \tag{$\ast$}<=
BR>\end{equation}<BR>Using ($\ast$) with $n =3D 45$, straightforward calcul=
ation gives<BR>\begin{align*}<BR>\sum_{k=3D0}^{89} \tan^2 \left( \frac{\pi(=
2k+1)}{180} \right) &amp; =3D<BR>\frac{1}{2} \sum_{k=3D0}^{89} \left\{&nbsp=
; \sec^2 \left(<BR>\frac{\pi(2k+1)}{180} \right)&nbsp; - 1 \right\} <A href=
=3D"file://\\[.1in">\\[.1in</A>]<BR>&amp; =3D \frac{1}{2} (90^2 - 90) =3D 4=
005.<BR>\end{align*}<BR>=3D=3D=3D <BR><BR>[]'s <BR>
Lu=EDs <BR>
<BLOCKQUOTE>
<HR>
From: npc1972@xxxxxxxxx<BR>To: obm-l@xxxxxxxxxxxxxx<BR>Subject: [obm-l] tri=
gonometria 2<BR>Date: Thu, 1 Nov 2001 03:25:29 -0200<BR><BR>
<META content=3D"Microsoft SafeHTML" name=3DGenerator>
<STYLE>
</STYLE>

<DIV><FONT face=3DArial size=3D2>
<P class=3DEC_MsoNormal><FONT face=3D"Times New Roman" size=3D3>Feras da li=
sta como fa=E7o issa?</FONT></P>
<P class=3DEC_MsoNormal><FONT face=3D"Times New Roman" size=3D3></FONT>&nbs=
p;</P>
<P class=3DEC_MsoNormal><FONT face=3D"Times New Roman" size=3D3>Prove que :=
 </FONT><SPAN style=3D"TOP: 5pt"><IMG height=3D27 src=3D"cid:000c01c16295$9=
ee6a790$396d51bd@pessoal2b51d2e" width=3D379></SPAN></P></FONT></DIV></BLOC=
KQUOTE><br /><hr />Not=EDcias direto do New York Times, gols do Lance, vide=
ocassetadas e muitos outros v=EDdeos no MSN Videos! <a href=3D'http://video=
.msn.com/?mkt=3Dpt-br' target=3D'_new'>Confira j=E1!</a></body>
</html>=

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