1. ## Compute N...

Compute N if:

N = 1 + 1/(2+1/(2+1/(2+...)))

P.S. This will probably be the last problem I will post for a long time, if again. Thank you all for all of your help. Without you, these problems would remain unsolved and I'd be in trouble.

2. Originally Posted by ceasar_19134
Compute N if:

N = 1 + 1/2+1/2+1/2+...
You're kidding right?

Let me try this. The question you REALLY want answered is:
N = 1 + 1/(2 + 1/(2 + 1/(2 + ...)))

-Dan

3. Yes what Dan said was right but could you answer the question

N = 1 + 1/(2 + 1/(2 + 1/(2 + ...)))

4. Whoops. Sorry.

My paper has it as a picture and I forgot I needed parenthesis.

"Either way"?

5. Originally Posted by Rimas
Yes what Dan said was right but could you answer the question

N = 1 + 1/(2 + 1/(2 + 1/(2 + ...)))
Assume this converges (in fact we know it does but I wont go into that now,
Put:

X = 1/(2 + 1/(2 + 1/(2 + ...)))

Then:

X= 1/(2+X),

or:

X^2+2X - 1=0

or X = [-2 +/- sqrt(4+4)]/2 = +/-sqrt(2)-1

but as we know X>0, we have X=sqrt(2)-1, so

N = 1 + 1/(2 + 1/(2 + 1/(2 + ...))) = 1 + X = sqrt(2)

RonL

6. I knew I had seen how to do this. I had just forgotten.

-Dan

7. The harder thing in this problem besides for the sum is to show it actually converges. But since this is a high school question we can ignore that.