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Mathemtical Induction

Posted June 6th, 2009 by alpha
in

Prove by the principle of mathematical induction that :n(n+1)(2n+1) is divisible by 6 for all values of $ n\in N $

please show all steps.
Thank You

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answer

On June 6th, 2009 Structure says:

n=1
1*2*3=6 is divisible by 6

suppose k(k+1)(2k+1)=6a
then
$ (k+1)(k+2)(2k+3)=(k+1)(k+2)(2k+3)-k(k+1)(2k+1)+6a=(k+1)(2k^2+7k+6-2k^2-k)+6a=6(k+1)^2+6a=6((k+1)^2+a) $
is also divisible by 6
Then for all n , n(n+1)(2n+1) is divisible by 6

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