Hello Bomba. Thanks for responding, you too Hurkyl. I know you're just telling me the minimum for my own good but you know what, I couldn't even get past the definition and I'd like to understand it. This is what I have:
If I start from [itex]R_0[/itex] and you say calculate R2, R4, R6,. . ., and the recursion relation is always in reference to R(n2), then it's just like doing it for each N and set up the relation for R(n1). Is that not correct? That is, if I start with [itex]R_0[/itex], then it seems to me, just ignore the odd members in the sequence. Perhaps that is not correct though. When I experiment with it though in Mathematica, say for R0=1.9, it doesn't seem to converge to the value you specify. This is how I set it up in Mathematica. Perhaps you can correct my interpretation:
[tex]f[x,xm1]=\sqrt{x+\sqrt{x\sqrt{xm1}}}[/tex];
[tex]xstart=1.9[/tex]
[tex]ntotal=alargenumber[/tex]
[tex]valist=Table[{0},{ntotal}][/tex]
[tex]valist[[1]]=f[xstart,xstart][/tex]
[tex]For[n=2,n<ntotal,n++,[/tex]
[tex]valist[[n]]=f[xstart,valist[[n1]]];[/tex]
When I do that, it seems to converge to 1.639 . . .
But:
[tex]\frac{1+\sqrt{4xstart3}}{2}=1.572...[/tex]
Would you (or Hurkyl or anyone else) tell me where my problem is?
Thanks,
Salty
Edit: corrected to reflect relation of even members in terms of R0
