

Title: MATHEMATICS Post by DOUBELL on Sep 1^{st}, 2011, 8:45am CAN SOMEONE PROVE BY Mathematical induction that (2r)^3 = 2 (n^2) (n+1)^2 . need help with this one. 

Title: Re: MATHEMATICS Post by towr on Sep 1^{st}, 2011, 8:52am I think you may have stated the problem incorrectly or incompletely. Since there seem to be no constraints on the values of r and n the two sides are plainly not equal for all values of n and r. 

Title: Re: MATHEMATICS Post by DOUBELL on Sep 1^{st}, 2011, 9:11am it is fact correct since for r=1 the LHs is (2)^3 = 8 AND FOR N =1 THE RIGHT HAND SIDE IS 2(1^2) (1+1)^2= 2 (2)^2 = 8. 

Title: Re: MATHEMATICS Post by pex on Sep 1^{st}, 2011, 11:41am I cannot find any other integer solutions than r=0, n=1 r=0, n=0 r=1, n=2 r=1, n=1. I don't see what mathematical induction could have to do with it, except perhaps in proving that there are no other solutions (or that there are, but I missed them). 

Title: Re: MATHEMATICS Post by ThudnBlunder on Sep 1^{st}, 2011, 12:22pm Maybe LHS should be http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/csigma.gif(2n^{3}) 

Title: Re: MATHEMATICS Post by pex on Sep 1^{st}, 2011, 12:31pm on 09/01/11 at 12:22:53, ThudnBlunder wrote:
I am impressed by your mindreading skills! 

Title: Re: MATHEMATICS Post by ThudnBlunder on Sep 1^{st}, 2011, 12:42pm on 09/01/11 at 12:31:09, pex wrote:
Thank you, pex. [fingernail_polishing_smiley] 

Title: Re: MATHEMATICS Post by towr on Sep 1^{st}, 2011, 12:52pm Ah, then it makes sense [hide]base case, http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif0..0 (2r)^{3} = 0 = 2 * 0^{2} * (0+1)^{2} induction under assumption it's true for every natural number smaller than n: http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif0..n (2r)^{3} = {move last term from sum} http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif0..n1 (2r)^{3} + (2n)^{3} = {invoke induction hypothesis} 2 * n^{2} * (n1)^{2} + 8n * n^{2} = {regroup terms} 2 * ((n1)^{2} + 4n) * n^{2} = {simplify} 2 * n^{2} * (n+1)^{2}[/hide] 

Title: Re: MATHEMATICS Post by DOUBELL on Sep 1^{st}, 2011, 1:52pm on 09/01/11 at 12:22:53, ThudnBlunder wrote:
THAT IS IN FACT CORRECT ABOUT THE LEFT HAND SIDE 

Title: Re: MATHEMATICS Post by Michael Dagg on Feb 29^{th}, 2012, 9:53pm Gee. One might ask if induction is valid within an induction argument itself. What you do think? 

Title: Re: MATHEMATICS Post by Jack Hadin on Oct 29^{th}, 2012, 11:13am I think you have recorded the problem wrongly or perhaps incompletely. Because on a search engine appear to be no constraints throughout the principles of r along with n the two sides tend to be plainly not equal for every one of the principles of n also as r. 

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