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Prove

Posted June 6th, 2009 by alpha
in

Given that $ 2.7^n+3.5^n-5 $ is divisible by 24 then prove that $ 2.7^{k+1}+3.5^{k+1}-5 $ is divisible by 24.

‹ Mathematical induction : Mathemtical Induction ›

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answer

On June 6th, 2009 Structure says:

$ 2.7^n+3.5^n-5 $ is divisible by 24 then prove that $ 2.7^{k+1}+3.5^{k+1}-5 $ is divisible by 24.
$ 2.7^{k+1}+3.5^{k+1}-5 =2.7^{k+1}+3.5^{k+1}-5 -(2.7^n+3.5^n-5)+2.7^n+3.5^n-5=14.7^n+15.5^n-2.7^n-3.5^n+24p=12.7^n+12.5^n+24p=12(7^n+5^n)+24p=12(2x+1+2y+1)+24p=24(x+y+1+p) $

~~THANK YOU ~~

On June 7th, 2009 alpha says:

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