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MathGroup Archive 2005

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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! 
> > 
> > 
> > 
> 


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