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Prove by induction that 13^n - 6^(n - 2) is divisible by 7, n subset N.
Step 1: n = 1...
13^1 - 6^(1 - 2) = 13 - 6^-1 = 13 - 0.1666 = 12.833
Can someone help me spot where I've gone wrong on the calcualtion to prove n = 1 yields a number divisible by 7?
Thank you.
I think you need to start from n=2.Quote:
Originally Posted by GrigOrig99
Thanks. I suppose it seems obvious, but all the examples in the book were operating from n = 1, so I figured I didn't have the choice.
Supposeis divisible by 7
Isalso divisible by 7 ?
so the inductive proof is verified.
You just need to know which value of n it becomes valid for.
Got it. Thanks.
Proof By Induction tries to show the following...
Proposition being true for n=a causes the proposition to be true for n=a+1,
being true for n=a+1 in turn causes it to be true for n=a+2,
being true for n=a+2 in turn causes it to be true for n=a+3,
which in turn causes it to be true for n=a+4,
which in turn causes it to be true for n=a+5,
which in turn...... all the way to infinity.
We show this for every pair of terms in general using n=k and n=k+1.
It's like Japanese dominoes.
The value "a" is most often 1, but may be otherwise.