Re: Re: How to compute this sum?

*To*: mathgroup at smc.vnet.net*Subject*: [mg63084] Re: Re: [mg63041] How to compute this sum?*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Tue, 13 Dec 2005 03:41:33 -0500 (EST)*Reply-to*: hanlonr at cox.net*Sender*: owner-wri-mathgroup at wolfram.com

I forgot to look at the limit of the first two terms. The sum appears to be 1. expr=(-6*2^n*n+3*2^n+2*3^n*n)/(3^n)/(n^2-3*n+2)/(2^n); Plot[Evaluate[expr],{n,0,5}, Epilog->{Red, AbsolutePointSize[4],Point/@({#,Limit[ expr,n->#]}&/@{1,2})}]; Total[Limit[expr,n->#]&/@{1,2}]+Sum[Evaluate[expr],{n,3,Infinity}]//Simplify 1 Bob Hanlon > > From: Bob Hanlon <hanlonr at cox.net> To: mathgroup at smc.vnet.net > Date: 2005/12/12 Mon AM 06:30:27 EST > To: "mizhael" <loseminds at hotmail.com>, <mathgroup at smc.vnet.net> > Subject: [mg63084] Re: [mg63041] How to compute this sum? > > expr=(-6*2^n*n+3*2^n+2*3^n*n)/(3^n)/(n^2-3*n+2)/(2^n); > > expr//FullSimplify > > (2*(-3*2^n + 3^n)*n + 3*2^n)/(6^n*((n - 2)*(n - 1))) > > The term is undefined for n equal to either 1 or 2. Excluding those terms, > > Sum[Evaluate[expr],{n,3,Infinity}] > > 1/6 > > > Bob Hanlon > > > > > From: "mizhael" <loseminds at hotmail.com> To: mathgroup at smc.vnet.net > > Date: 2005/12/11 Sun PM 10:25:16 EST > > Subject: [mg63084] [mg63041] How to compute this sum? > > > > sum((-6*2^n*n+3*2^n+2*3^n*n)/(3^n)/(n^2-3*n+2)/(2^n),n = 1 .. Inf) > > > > thanks a lot! > > > > > > >