http://mathfactor.uark.edu/2008/08/follow-up-the-harmonic-series/ The Math Factor Podcast Site Sat, 21 Nov 2009 21:45:21 -0600 http://wordpress.org/?v=2.8.5 hourly 1 http://mathfactor.uark.edu/2008/08/follow-up-the-harmonic-series/comment-page-1/#comment-365 tricycle Thu, 21 Aug 2008 22:02:01 +0000 http://mathfactor.uark.edu/?p=245#comment-365 It seems to me that a natural assumption would be that when the rope is stretched, that it is stretched uniformly. The discussion seems to assume that only the part stretched is the rope in front of the worm with the position of the worm being fixed, i.e., after the rope is stretched to 2 m the worm is still at 1 cm instead of being proportionally stretched to 2 cm. Taking into account this additional boost leads to the recursive position at the start of each second: p(0) = 0 and p(n) = (p(n-1)+1)(n+1)/n with the length of the rope l(n) = 100(n+1) where all of the units are cm. Is there a nice closed form for this recursion? It seems to me that a natural assumption would be that when the rope is stretched, that it is stretched uniformly. The discussion seems to assume that only the part stretched is the rope in front of the worm with the position of the worm being fixed, i.e., after the rope is stretched to 2 m the worm is still at 1 cm instead of being proportionally stretched to 2 cm. Taking into account this additional boost leads to the recursive position at the start of each second: p(0) = 0 and p(n) = (p(n-1)+1)(n+1)/n with the length of the rope l(n) = 100(n+1) where all of the units are cm. Is there a nice closed form for this recursion?

]]> http://mathfactor.uark.edu/2008/08/follow-up-the-harmonic-series/comment-page-1/#comment-362 strauss Sun, 17 Aug 2008 18:49:00 +0000 http://mathfactor.uark.edu/?p=245#comment-362 Incidentally, our post <a href="http://mathfactor.uark.edu/2006/11/10/an-astronomical-cost/" rel="nofollow">BM. An astronomical cost!</a> also involves the harmonic series and some close relatives. This is how I was able to make rough estimates of the number of bananas required, without using a calculator! Incidentally, our post BM. An astronomical cost! also involves the harmonic series and some close relatives. This is how I was able to make rough estimates of the number of bananas required, without using a calculator!

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