Well, yes, I know the answer is sqrt(2)/2. What I don't know is how to prove it.
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Wouter Meeussen Sent: Saturday, July 05, 2014 12:48 PM To: math-fun Subject: Re: [math-fun] Problem I never solved
nice!
prod( k=1..m, A026147(k) ) / prod( k=1..m, A181155(k) ) approaches sqrt( 2 ) as m-> infinity
goes like 1, 1/2, 2/3, 7/10, 286/405, 144305/204102, 276620298878/391202754597, ...
(* those who abhor Mathematice lines, please look away : *)
k=1/2;NestList[#/(#/. i->i+(k=2k))&,x[i],6] %/. x[i_]->i %/. i->1 %//N
Wouter.
-----Original Message----- From: David Wilson Sent: Saturday, July 05, 2014 5:34 PM To: math-fun Subject: [math-fun] Problem I never solved
I know the answer to this, but not how to derive it:
What is the value of
(((1/2)/(3/4))/((5/6)/(7/8)))/...
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