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Let A_1=1, let A_(n+1) = sum(k=1...n) of 1/(A_k).
So the series goes 1, 1, 2, 2.5, 2.9, ~3.244827586 , etc. I'm trying to figure out it this is logarithmic and if so how. If I want to find A_1000000, does anyone have any better idea than an excel spreadsheet? (A1 set to 1, B1 and below set to =1/A1 , A2 and below =sum($B$1:$B1) ) Naraht ( talk) 05:01, 26 October 2015 (UTC)
res=1.0 tel=13 while tel<=1000000: res=res+(1.0/res) tel=tel+1 print(res)
Given that the previous one could be expressed as A_(n+1)=A_n + 1/A_n , I'm now wondering about the behavior of A_(n+1)=A_n - 1/A_n. Presuming that A_1 is not equal to 1 or -1, this should never go to 0 (and then infinity), but the behavior seems Chaotic (and I mean that in the mathematical sense). I set 10 as the first value, and it decreases gradually until it drops below 1 and jumps to something with a much larger absolute value, decends again and jumps back out. Any feelings on this?
Hello,
I'm currently stuck with an analysis exercise. If , (with U open, bounded and with boundary) and , I'm meant to show the existence of a constant C such that .
I originally thought this would be a typical integration by parts question, but I can't see how to do it in this case since u doesn't necessarily have compact support. Aside from Poincare's inequality, I also don't know of any other inequalities relating a function with its derivative, so I'm lost at how to attack it. Also the fact that there are two constants on the right hand side, one of which we can control makes me think I'll need to use Cauchy's or Young's inequality with , but cannot see how at this stage it'd be useful.
Any advise/help?
Cheers,
Neuroxic ( talk) 07:44, 26 October 2015 (UTC)
Mathematics desk | ||
---|---|---|
< October 25 | << Sep | October | Nov >> | October 27 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Let A_1=1, let A_(n+1) = sum(k=1...n) of 1/(A_k).
So the series goes 1, 1, 2, 2.5, 2.9, ~3.244827586 , etc. I'm trying to figure out it this is logarithmic and if so how. If I want to find A_1000000, does anyone have any better idea than an excel spreadsheet? (A1 set to 1, B1 and below set to =1/A1 , A2 and below =sum($B$1:$B1) ) Naraht ( talk) 05:01, 26 October 2015 (UTC)
res=1.0 tel=13 while tel<=1000000: res=res+(1.0/res) tel=tel+1 print(res)
Given that the previous one could be expressed as A_(n+1)=A_n + 1/A_n , I'm now wondering about the behavior of A_(n+1)=A_n - 1/A_n. Presuming that A_1 is not equal to 1 or -1, this should never go to 0 (and then infinity), but the behavior seems Chaotic (and I mean that in the mathematical sense). I set 10 as the first value, and it decreases gradually until it drops below 1 and jumps to something with a much larger absolute value, decends again and jumps back out. Any feelings on this?
Hello,
I'm currently stuck with an analysis exercise. If , (with U open, bounded and with boundary) and , I'm meant to show the existence of a constant C such that .
I originally thought this would be a typical integration by parts question, but I can't see how to do it in this case since u doesn't necessarily have compact support. Aside from Poincare's inequality, I also don't know of any other inequalities relating a function with its derivative, so I'm lost at how to attack it. Also the fact that there are two constants on the right hand side, one of which we can control makes me think I'll need to use Cauchy's or Young's inequality with , but cannot see how at this stage it'd be useful.
Any advise/help?
Cheers,
Neuroxic ( talk) 07:44, 26 October 2015 (UTC)