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chingching
Joined: 17 Nov 2004Posts: 13
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Posted: Mon Apr 18, 2005 5:22 pm Post subject: also a prove problem ~~”””
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prove by M.I that
1^3+2^3+3^3+………+(2n)^3=n^2(2n+1)^2 for any positive integer n
hence find the sum of
1^3+3^3+5^3+……+(2n-1)^3
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Cube
Joined: 16 Feb 2005Posts: 16
Location: Hong Kong
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Posted: Mon Apr 18, 2005 7:31 pm Post subject:
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But the proportion is not true when n=1, are you have some typing error?
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Soarer
Frequent VisitorJoined: 18 Jan 2004Posts: 257
Location: Hong Kong
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Posted: Mon Apr 18, 2005 7:59 pm Post subject:
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why is the proposition false when n=1? It’s true.
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wilson
Frequent VisitorJoined: 20 Oct 2004Posts: 94
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Posted: Tue Apr 19, 2005 1:18 pm Post subject: Re: also a prove problem ~~”””
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(i) To prove :
For , L.H.S.R.H.S.
Assume for ,
For ,
L.H.S.
(By assumption)
= R.H.S. Proved.
(ii)
For ,
For ,
As a whole, for positive integer n,
(iii)
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chingching
Joined: 17 Nov 2004Posts: 13
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Posted: Tue Apr 19, 2005 8:57 pm Post subject: thx
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thank you ar
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Chan Pak Keung
Frequent VisitorJoined: 09 May 2004Posts: 22
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Posted: Thu Apr 28, 2005 3:13 am Post subject: Re: also a prove problem ~~”””
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chingching wrote:
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prove by M.I that
1^3+2^3+3^3+………+(2n)^3=n^2(2n+1)^2 for any positive integer n
hence find the sum of
1^3+3^3+5^3+……+(2n-1)^3
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我再次嚴正聲明, 請各位遵守規守 ! 這問題只有中四程度, 是 Additional Maths 吧 ! 請不要把它放在 ADVANCDED MATHS 這 Forum 裏 !
我不想再薑H, 面斥不雅 !!!
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