Comments on: EV. What’s the Difference? http://mathfactor.uark.edu/2008/12/ew-whats-the-difference/ The Math Factor Podcast Site Fri, 08 Aug 2014 12:52:06 +0000 hourly 1 https://wordpress.org/?v=4.9.25 By: prunthaban http://mathfactor.uark.edu/2008/12/ew-whats-the-difference/comment-page-1/#comment-415 Tue, 30 Dec 2008 07:58:53 +0000 http://mathfactor.uark.edu/?p=314#comment-415 An attempted solution,
This looks like a discrete version of Mclaurin series…
The result looks like, f(x) = a1 + C(x,1)*a2 + C(x, 2) * a3…..C(x,n-1) * an

Here C(n,c) is the binomial coefficient. a1, a2… an are the given numbers in the first column.

Technically speaking in my formula f(0) will be the first term and not f(1). I hope that does not matter. Otherwise I just need to use (x-1) in place of x and will make the formula ugly. By the way, is there are better simplification than this? Not sure.

]]> By: strauss http://mathfactor.uark.edu/2008/12/ew-whats-the-difference/comment-page-1/#comment-425 Mon, 29 Dec 2008 00:04:20 +0000 http://mathfactor.uark.edu/?p=314#comment-425 Hi, eab and tricycle are perfectly correct! eab’s first comment prompted me to fix the typo– his glasses are fine!!

]]> By: eab http://mathfactor.uark.edu/2008/12/ew-whats-the-difference/comment-page-1/#comment-414 Sat, 27 Dec 2008 15:29:29 +0000 http://mathfactor.uark.edu/?p=314#comment-414 Hmm . . . I guess my glasses were dirty last night when I looked at this since the numbers are 2, 3, 11 and not 2, 9 . . . Please disregard earlier comment.  I got it.

]]> By: eab http://mathfactor.uark.edu/2008/12/ew-whats-the-difference/comment-page-1/#comment-413 Sat, 27 Dec 2008 05:09:28 +0000 http://mathfactor.uark.edu/?p=314#comment-413 I’m unclear on how this works . . . (9-2) is 7, not 1.  If we take the differences from the first series, we don’t get 1.  If given 2, 1 and 7 as a column, I can see how we generate  8,15 etc. but when we go up the next row, I see the 9, 17, etc but if we’re given the 2 and the 1, I don’t see how we can solve it.  What am I missing?  Thanks.

]]> By: tricycle http://mathfactor.uark.edu/2008/12/ew-whats-the-difference/comment-page-1/#comment-412 Tue, 23 Dec 2008 06:49:15 +0000 http://mathfactor.uark.edu/?p=314#comment-412 There is a typo  in reconstructing the values in the first row. They should be 2,3,11,26,48,. . .  (It looks like someone added 1+8 instead of 1+2). 
 The polynomial is quadratic and can then easily be found by using the column before 2,1,7, namely 8,-6, 7. The polynomial is 8 C(n,0) -6 C(n,1) +7 C(n,2) = 8 – 19n/2 +7n^2/2. Alternatively use 2,1,7 and replace n with n-1.

]]>