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Hey! Thanks in advace for any help with this one :)
 

Prove, by method of induction that 3^(3n)+2(n+2) is divisible for 5 for all nEN.

 

I've had a go- but can't manage to get anywhere.

Thanks!

 

-C

 Feb 21, 2020
 #1
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It's not true!  Set n = 2

 

3^(3*2) + 2*(2+2) = 3^6 + 8 = 737  which is not divisible by 5.

 

On the other hand, if this is meant to be 3^(3n) + 2^(n+2) then:

 

First step:

With n= 1:

3^(3*1) + 2^(1+2) = 27 + 8 = 35, so divisible by 5.

 

Second step:

Let m = 3^(3n) + 2^(n+2)

Prove that it's true for n+1 if it's true for m.

 

3^(3n+3) + 2^(n+1+2) = 27*3^(3n) + 2*2^(n+2) = 25* 3^(3n) + 2*m

 

Since 5 divides 25 and m, and it's true when n=1, it is true for all n.

 Feb 21, 2020
edited by Alan  Feb 21, 2020
 #2
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+1

Thankyou! That is what I meant :)

Guest Feb 21, 2020

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