Re: Differences between recursions and limit

*To*: mathgroup at smc.vnet.net*Subject*: [mg60576] Re: Differences between recursions and limit*From*: "shizp" <shizp at 263.net>*Date*: Tue, 20 Sep 2005 06:16:19 -0400 (EDT)*References*: <dgm01k$njm$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hello, In the first method,it must calculate x[k-1] again when every time it calculates x[k].So the recursion is slow.But in the second one,x[k-1] is saved in the memory,namely a.So it can be called straightforward from memory,need not calculate again. as regards the limit of this recursion for k->Infinite,you can try this: FixedPoint[0.25(1 + # + #^2 + #^3) &, 0]