Thanks in advance!

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- April 7th 2008, 03:06 PMshawnFunction Question
Thanks in advance!

- April 7th 2008, 03:36 PMPlato
How much of this have you done?

Have you done any of it?

If you have, what pattern do you see? - April 7th 2008, 03:49 PMshawn
- April 7th 2008, 04:24 PMtopsquark
- April 7th 2008, 04:35 PMshawn
- April 8th 2008, 08:23 PMshawnInductive Proof
I'm doing part c now,

Basis is easy when k = 3.

Inductive step

Let x >=3 be an integer.

Our IH is (from the formula's I found for part b)

f^x (n) = n + x when x is even, and

f^x (n) = n + x + 2(-1)^n when x is odd

We want to prove that

f^x+1(n)=n+x+1 when x+1 is even, and

f^x+1(n)=n+x+1+2(-1)^n when x+1 is odd

**Is the above correct?**

So we have two cases from here:

**Case 1**: when x+1 is even, x is odd

Now, f^x+1(n) = f(f^x(n)) = f(n +x + 2(-1)^n)

Now, I think we have two more sub cases but I'm not sure?

**Case 2**: when x+1 is odd, x is even

Now, f^x+1(n) = f(f^x(n)) = f(n + x)

Now, I think we have two more sub cases but I'm not sure?

Can someone help me finish the sub cases?

Thanks!