bob012345's latest activity

In post #17, I gave an accelerator that works well on an alternating series like the golden ratio. The accelerator takes three...

If one takes the Golden Ladder equation ##R^2 -R -1=0## and instead of solving it exactly, write it as ##R = \sqrt{1+R}## then start...

Yes @Baluncore, that is what I found, and I put in the figure above. In fact, the continued fraction that computes the equivalent...

I like this problem. It overturns every assumption we would normally make.

I was wrong to say changing the tail doesn’t change the ladder but like I said, it literally changes the ladder to be a different...

Ok, but then changing the tail to low values is changing the problem significantly. It no longer the ‘tail’ but a different ladder.

It makes a difference for a zero ohm termination = tail. Changing the tail, the starting value for evaluation, of a 100 term ladder...

Which circuit are you simulating with 100 stages? Our original ladder in post #1 or your ladder? Not sure what you mean by “changing the...

Welcome to PF! I believe you are solving a different ladder that goes like this: The ladder being studied in this thread has the...

Here are recursion relations that give the exact polynomials for the numerator and denominator for any ladder with ##N## stages and a...

Doing that derives the limiting term as ##0.9⋅10^n## discussed in post #8.

I believe if it’s transcendental it is also irrational.

And it may be rational, irrational and if irrational it may be expressible as a compact, exact quantity involving a square root or it...

For the original infinite ladder in post #1 I have found that the number of digits in ##p## and ##q## goes as ##1+n(n-1)## as in post #5...

BTW, the reverse ladder, where the horizontal resistors are large and the vertical resistors are small, converges super fast with no...