       Re: convert an expression to an infinite series

• To: mathgroup at smc.vnet.net
• Subject: [mg29622] Re: [mg29618] convert an expression to an infinite series
• From: BobHanlon at aol.com
• Date: Fri, 29 Jun 2001 01:35:55 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```In a message dated 2001/6/28 5:42:56 AM, meshii at mech.fukui-u.ac.jp writes:

>Does anyone know a way to convert an expression to an infinite series?
>Let me show the idea by a concrete problem.
>
>In:=
>Sum[E^(-2*m*n*L), {n, 0, Infinity}]
>
>Out=
>E^(2*L*m)/(-1 + E^(2*L*m))
>
>Yes, Mathematica 4.1 knows that the infinite sum converges to a specific
>value.
>Then, my question is that how can I expand the expression
> E^(2*L*m)/(-1 + E^(2*L*m))
>in an infinite series on n, in this case
> Sum[E^(-2*m*n*L), {n, 0, Infinity}]
>
>Is there any way or is it an one way path?
>

Solve[Sum[y^n, {n, 0, Infinity}] == E^(2*L*m)/(-1+E^(2*L*m)), y]

{{y -> E^(-2*L*m)}}

Bob Hanlon
Chantilly, VA  USA

```

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