tag:blogger.com,1999:blog-2433841880619171855.post166533381472707602..comments2021-10-20T11:15:04.744+01:00Comments on Pat'sBlog: Plus or Minus InfinityUnknownnoreply@blogger.comBlogger5125tag:blogger.com,1999:blog-2433841880619171855.post-2887700210367569732011-01-14T21:27:02.728+00:002011-01-14T21:27:02.728+00:00Ok, I think I understand.... The derivation goes l...Ok, I think I understand.... The derivation goes like this:<br />if the value of the constant was a and the sum of the iteration is N, then N^2 = a +N.... <br /><br />I presumed that a>0, but if it was equal to zero, then we have N^2 = N, which is only true when N=0 or N=1<br />Hope that helps.Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-14189038515875092792011-01-14T21:02:05.495+00:002011-01-14T21:02:05.495+00:00Looking at the solution a little harder now, it se...Looking at the solution a little harder now, it seems it stems from the fact we're using the quadratic formula for the solution to the infinite radical. <br /><br />The infinite radical actually has 2 solutions: [1 + sqrt(4n+1)]/2 AND [1 - sqrt(4n+1)]/2. That second solution gives 0 when n=0, which is what I would expect, however there is still this other solution of 1 that is very puzzling. Your thoughts are appreciated.Taylorhttps://www.blogger.com/profile/15436989339250022436noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-59073246787089434332011-01-14T20:45:13.121+00:002011-01-14T20:45:13.121+00:00Hey Pat,
Sorry for the ambiguity.
Say you have a...Hey Pat,<br /><br />Sorry for the ambiguity.<br /><br />Say you have a radical like the second image in this post:<br /><br />sqrt(n+sqrt(n+sqrt(n+sqrt(n+...)))<br /><br />You've shown that this is equal to [1 + sqrt(4n+1)]/2<br /><br />Now, say you let n=0, then the infinite radical is then equal to [1 + sqrt(4n+1)]/2 = [1 + sqrt(4(0)+1)]/2 = [1 + sqrt(1)]/2 = [1+1]/2 = 1<br /><br />Hope that helps!Taylorhttps://www.blogger.com/profile/15436989339250022436noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-72083048617319745632011-01-14T19:06:18.906+00:002011-01-14T19:06:18.906+00:00Taylor,
Thanks for the kind comments... I'm n...Taylor, <br />Thanks for the kind comments... I'm not sure I caught which infinite radical you mean.... or why you get one... help me see what you mean and maybe I can be more help...Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-77197985076241703762011-01-14T18:43:30.882+00:002011-01-14T18:43:30.882+00:00Everytime I've seen this infinite radical writ...Everytime I've seen this infinite radical written out, I've always plugged n=0 into the equation which results in an answer of 1! Any quick explanation of why that might be?<br /><br />Oh, love the blog. Was pointed to it today and have been reading back over older articles.Taylorhttps://www.blogger.com/profile/15436989339250022436noreply@blogger.com