       Re: Bug in SymbolicSum, or am I just stupid?

• To: mathgroup at smc.vnet.net
• Subject: [mg5637] Re: [mg5593] Bug in SymbolicSum, or am I just stupid?
• Date: Wed, 1 Jan 1997 21:05:01 -0500
• Organization: Saguaro Software
• Sender: owner-wri-mathgroup at wolfram.com

```Sean Luke wrote:
>
> I'm wondering if I'm just doing something really dumb, or if there
> is some profound reason why Mathematica 2.2 seems to be finding different
> symbolic infinite sumations for the same expression:
>
> Mathematica 2.2 for SPARC
> Copyright 1988-94 Wolfram Research, Inc.
>  -- Terminal graphics initialized --
>
> In:= <<Algebra`SymbolicSum`
>
> In:= ?SymbolicSum
> SymbolicSum[f, {i, imin, imax}] attempts to find the value of Sum[f, {i, imin,
>    imax} ] for symbolic imin,imax. SymbolicSum[f, {i, imax}] evaluates the sum
>    of f with i running from 1 to imax.
>
> In:= Simplify[(2)( 1/(2^n )  - ((n+1)/2)(1/(2^n))]  (* expression 1 *)
>
>         3 - n
> Out= -----
>            n
>         2 2
>
> In:= Simplify[(2 - (n+1)/2) (1/(2^n))]  (* expression 2--should be same *)
>
>         3 - n
> Out= -----
>            n
>         2 2
>
> In:= SymbolicSum[(2)( 1/(2^n) ) - ((n+1)/2)(1/(2^n)),{n,1,Infinity}]  (*1*)
>
>         1
> Out= -
>         2
>
> In:= SymbolicSum[(2 - (n+1)/2) (1/(2^n)),{n,1,Infinity}]  (*2*)
>
>           3
> Out= -(-)
>           4
>
> In:= SymbolicSum[Out,{n,1,Infinity}]   (* simplified *)
>
>           3
> Out= -(-)
>           4
>
> Thanks very much anyone.  Sorry if this is a FAQ or obnoxious newbie question.
>
> Sean Luke
> U Maryland at College Park, very late a night
> seanl at cs.umd.edu

This looks like a bug in 2.2:

Mathematica 2.23 under Windows 95 gives

In:= <<Algebra`SymbolicSum`

In:= SymbolicSum[(3-n)/2^(n+1),{n,1,Infinity}]

3
Out= -(-)
4

while Mathematica 3.0 (which has apparently incorporated
the SymbolicSum functionality into Sum) gives

In:= Sum[(3-n)/2^(n+1),{n,1,Infinity}]

1
Out= -
2

which is clearly the correct answer