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# Proof by induction help watch

1. Hi I had to prove by induction that 12^n +2 x 5^(n-1) is divisible by 7

I have got to [12^(k+1) + 2 x 5^k] -5[12^k +2 x 5^(k-1)]

Stupid thing is i dunno how to bloody multiply out -5[12^k +2 x 5^(k-1)]. Any help would be much appreciated! Step by step would be wonderful haha

EDIT: do I multiply the -5 to the k-1 to make K?!
2. Instead of trying to expand your f(k) to be of the same index as f(k+1), consider doing it the other way around.
3. (Original post by bonana567)
Hi I had to prove by induction that 12^n +2 x 5^(n-1) is divisible by 7

I have got to [12^(k+1) + 2 x 5^k] -5[12^k +2 x 5^(k-1)]

Stupid thing is i dunno how to bloody multiply out -5[12^k +2 x 5^(k-1)]. Any help would be much appreciated! Step by step would be wonderful haha

EDIT: do I multiply the -5 to the k-1 to make K?!

well, it should have already been shown for

so the right side divides.

I think?

_Kar.
4. f(k) = 12^k + 2x5^(k-1)
f(k+1) = 12^(k+1) + 2x5^(k)

f(k+1) - 5f(k)

[12^(k+1) + 2x5^(k)] - 5[12^k + 2x5^(k-1)]
= 12 x 12^k + 2x5^k - 5x12^k -2x5^k
= 7x12^k (divisible by 7)

Since by assumption 7 | f(k) is true
then 7 | f(k+1) is also true

therefore by PMI, 7 divides 12^k + 2x5^(k-1) etc etc.

(sorry I can't write Latex, hope this helps

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