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chingching
Joined: 17 Nov 2004Posts: 12

Posted: Mon Apr 18, 2005 5:22 pm Post subject: also a prove problem ~~”””



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+……+(2n1)^3





Cube
Joined: 16 Feb 2005Posts: 12
Location: Hong Kong

Posted: Mon Apr 18, 2005 7:31 pm Post subject:



But the proportion is not true when n=1, are you have some typing error?





Soarer
Frequent VisitorJoined: 18 Jan 2004Posts: 218
Location: Hong Kong

Posted: Mon Apr 18, 2005 7:59 pm Post subject:



why is the proposition false when n=1? It’s true.





Wilson
Frequent VisitorJoined: 20 Oct 2004Posts: 83

Posted: Tue Apr 19, 2005 1:18 pm Post subject: Re: also a prove problem ~~”””



(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)





