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Topic: MATHEMATICS (Read 8073 times) 

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


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towr
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Re: MATHEMATICS
« Reply #1 on: Sep 1^{st}, 2011, 8:52am » 
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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.


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DOUBELL
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Re: MATHEMATICS
« Reply #2 on: Sep 1^{st}, 2011, 9:11am » 
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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.


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pex
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Re: MATHEMATICS
« Reply #3 on: Sep 1^{st}, 2011, 11:41am » 
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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).


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ThudnBlunder
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Re: MATHEMATICS
« Reply #4 on: Sep 1^{st}, 2011, 12:22pm » 
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Maybe LHS should be (2n^{3})


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pex
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Re: MATHEMATICS
« Reply #5 on: Sep 1^{st}, 2011, 12:31pm » 
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on Sep 1^{st}, 2011, 12:22pm, ThudnBlunder wrote:Maybe LHS should be (2n^{3}) 
 I am impressed by your mindreading skills!


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ThudnBlunder
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Re: MATHEMATICS
« Reply #6 on: Sep 1^{st}, 2011, 12:42pm » 
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on Sep 1^{st}, 2011, 12:31pm, pex wrote: I am impressed by your mindreading skills! 
 Thank you, pex. [fingernail_polishing_smiley]

« Last Edit: Sep 1^{st}, 2011, 4:01pm by ThudnBlunder » 
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towr
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Re: MATHEMATICS
« Reply #7 on: Sep 1^{st}, 2011, 12:52pm » 
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Ah, then it makes sense base case, 0..0 (2r)^{3} = 0 = 2 * 0^{2} * (0+1)^{2} induction under assumption it's true for every natural number smaller than n: 0..n (2r)^{3} = {move last term from sum} 0..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}

« Last Edit: Sep 1^{st}, 2011, 12:54pm by towr » 
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DOUBELL
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Re: MATHEMATICS
« Reply #8 on: Sep 1^{st}, 2011, 1:52pm » 
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on Sep 1^{st}, 2011, 12:22pm, ThudnBlunder wrote:Maybe LHS should be (2n^{3}) 
 THAT IS IN FACT CORRECT ABOUT THE LEFT HAND SIDE


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


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Jack Hadin
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Re: MATHEMATICS
« Reply #10 on: Oct 29^{th}, 2012, 11:13am » 
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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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