1. Good-Luck Nicolase!

2. Hrm doing the same thing for an=1+(-1)^N I get
an=1+(-1)^n
a1=1+(-1)^1=0
a2=1+(-1)^2=2
a3=1+(-1)^3=0
a4=1+(-1)^4=2

but when I tried following what you have done I end up, again, unbalanced.
1+(-1)^n=1+(-1)^n+1 (I assumed) Will check in the morning, brain about to explode. thanks again.

3. Still have an issue with the last message posted. Am I correct in saying that the ratio is: 2?

4. Originally Posted by Nickolase
Still have an issue with the last message posted. Am I correct in saying that the ratio is: 2?

Hmmm...

Look at this:

$a_{n+1}+a_n=2$

seems me right...

Prove it! You know how!

5. Originally Posted by Nickolase
Give a recursive definition of the sequence {an},n=1,2,3.....if an=4n-2 (The An's are sub n's, just not sure how to do that yet) all the information that is given. If necessary I can post the other similar problem with answer.
Find that: $a_1=2,~a_2=6,~a_3=10$.
So it seems that $a_1=2$ and if $n>1$ then $a_n=a_{n-1}+4$.

6. Originally Posted by Also sprach Zarathustra
Hmmm...

Look at this:

$a_{n+1}+a_n=2$

seems me right...

Prove it! You know how!
This brings up one of the questions that confuses me. Can I use induction to prove recursive? Or are the two completely unrelated? Also. it seems that while I was able to do the work, my remaining confusion seems to be the manner in which the formula is expressed when finished, which seems different than what I started with. I don't believe it matters as the other examples in the section seem to be looking for the ratio: which I believe to be correct. However, I want to know for the sake of knowing because while passing the course is the priority, full understanding is the goal. I dislike being on the outside looking in.

Itried to use induction but it doesn't seem to add up correctly so either I can't do it, or I'm doing something wrong almost immediately.

p(1) 1+2+3...1+(-1)^1=1
0=1 False but true if p(0)

7. I think it's depends when or where use induction...

Usually in this type of questions better use these steps...

If you had some $a_n=f(n)$ : ( $a_n$ is not in recursive form) and you need to find a recursive formula for $a_n$.

So, first of all: Try to find a pattern

second: try to guess recursive formula!

third: Check if your guess been successful guess by "putting" your $a_n=f(n)$

------------------------------------------------------------------------

$a_n=1+(-1)^n$

so, our sequence is: $0,2,0,2,0,...$

Finding pattern:

We can see that:

$a_2-a_1=2$
$a_4-a_3=2$

Now is the time for guessing!

We guess that our recursive formula(s) looks like: $a_{n+2}=a_n$

with $a_0=2$ and $a_{n+3}=a_{n+1}$

with $a_0=0$

To prove these formulas you need to substitute $a_n=1+(-1)^n$ in each of them.

I hope you understood something from all this...

8. Thanks to everyone. It may not seem like I'm getting it, but I am, slowly but surely. Problem with that statement is that it is a six week course.

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