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[SPAM] [obm-l] Diferença finita ( de novo)
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Essa sequecncia foi resolvida Pelo Professor Lu=EDs lopes (em 2003)de =
maneira brilhante, muito mais eficaz do que diferen=E7a finita.
Pergunto ao Professor ou os demais da lista.Como demonstrar as =
f=F3rmulas que est=E3o em negritos a abaixo.=20
1)Seja a PA de ordem 3
1,3,19,61,141,271,... a_i
Vamos gerar outras PAs fazendo a_{i+1} - a_i:
2,16,42,80,130 Delta a_i
14,26,38,50 Delta^2 a_i
12,12,12 Delta^3 a_i
a_i =3D a_1 + Delta a_1 binom(i-1,1) + Delta^2 a_1
binom(i-1,2) + Delta^3 a_1 binom(i-1,3)
a_i =3D 1 + 2(i-1) + 14(i-1)(i-2)/2 + 12(i-1)(i-2)(i-3)/6
a_i =3D 2i^3 - 5i^2 + 3i + 1
S_n =3D a_1 binom(n,1) + Delta a_1 binom(n,2) +
Delta^2 a_1 binom(n,3) + Delta^3 binom(n,4)
S_n =3D n[3n^3 - 4n^2 - 3n + 10] / 6
2) Posso reslver da mesma forma a seguinte quest=E3o (arrumando)
Determine o termo geral da sequ=EAncia { 3, 0, 5, 34 , 135, =
452........} e calcule em seguida a soma dos n primeiros termos.
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<!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 6.00.2900.2180" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>Essa sequecncia foi resolvida Pelo =
Professor Lu=EDs=20
lopes (em 2003)de maneira brilhante, muito mais eficaz do que =
diferen=E7a=20
finita.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Pergunto ao Professor ou os demais da =
lista.Como=20
demonstrar as f=F3rmulas que est=E3o em negritos a =
abaixo. </FONT></DIV>
<DIV> </DIV>
<DIV>1)Seja a PA de ordem =
3<BR><BR>1,3,19,61,141,271,... =20
a_i<BR><BR>Vamos gerar outras PAs fazendo a_{i+1} -=20
a_i:<BR><BR>2,16,42,80,130 Delta=20
a_i<BR>14,26,38,50 =
Delta^2=20
a_i<BR>12,12,12 &nbs=
p; =20
Delta^3 a_i<BR><BR><STRONG>a_i =3D a_1 + Delta a_1 binom(i-1,1) + =
Delta^2=20
a_1<BR>binom(i-1,2) + Delta^3 a_1 binom(i-1,3)<BR></STRONG>a_i =3D 1 + =
2(i-1) +=20
14(i-1)(i-2)/2 + 12(i-1)(i-2)(i-3)/6<BR>a_i =3D 2i^3 - 5i^2 + 3i +=20
1<BR><BR><STRONG>S_n =3D a_1 binom(n,1) + Delta a_1 binom(n,2) =
+<BR>Delta^2 a_1=20
binom(n,3) + Delta^3 binom(n,4)<BR></STRONG><BR>S_n =3D n[3n^3 - 4n^2 - =
3n + 10] /=20
6</DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>2) Posso reslver da mesma forma a =
seguinte quest=E3o=20
(arrumando)</FONT><BR><FONT face=3DArial size=3D2></FONT></DIV>
<DIV><FONT face=3DArial =
size=3D2> =20
Determine o termo geral da sequ=EAncia { 3, 0, 5, 34 , 135, =
452........} e=20
calcule em seguida a soma dos n primeiros termos.</FONT></DIV>
<DIV> </DIV></BODY></HTML>
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