       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,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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