Re: Limit of sequence

*To*: mathgroup at smc.vnet.net*Subject*: [mg25298] Re: [mg25276] Limit of sequence*From*: BobHanlon at aol.com*Date*: Tue, 19 Sep 2000 03:45:20 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

In a message dated 9/17/2000 5:54:09 PM, none at none.com writes: >Can Mathematica find the limit of a sequence? >As I understood, it treats the argument of the Limit function as a real >variable, >therefore the limit of Sin[Pi*n] turns out to be undefined. > Simplify[Sin[Pi*n], Element[n, Integers]] 0 As an example of finding the limit of a sequence: Needs["DiscreteMath`RSolve`"] Let eqn = {a[n] == a[n - 1] + a[n - 2], a[0] == a[1] == 1}; and the sequence for which the limit is desired be a[n]/a[n-1] soln = (a[n] /. (RSolve[eqn, a[n], n] // Flatten)) (2^(-1 - n)*(-(1 - Sqrt[5])^(1 + n) + (1 + Sqrt[5])^(1 + n)))/Sqrt[5] ratio = soln/(soln /. n -> (n - 1)); lim = Limit[ratio, n -> Infinity] 1/2*(1 + Sqrt[5]) FullSimplify[lim - GoldenRatio] == 0 True Bob Hanlon