Prove that 9 is a factor of:

P(n): for all positive integer n

Using the induction method,

I have proven P(1) to be true

P(k):

P(k+1):

How do I continue? I am new at doing proofs (Worried)

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- April 9th 2011, 05:13 PMmushroomProve that 9 is a factor of...
Prove that 9 is a factor of:

P(n): for all positive integer n

Using the induction method,

I have proven P(1) to be true

P(k):

P(k+1):

How do I continue? I am new at doing proofs (Worried) - April 9th 2011, 05:31 PMLoblawsLawBlog
Do you have to use induction? Sometimes that's tedious for problems like this. I would try to rewrite 10 as 9+1 and then use the binomial theorem.

- April 9th 2011, 05:33 PMmushroom
Yes, unfortunately it is required to use the induction method.

- April 9th 2011, 06:54 PMtopsquark
- April 9th 2011, 09:49 PMSoroban
Hello, mushroom!

Quote:

. .

. . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . . . . . .

We have proved statement

The inductive proof is complete.