       convert an expression to an infinite series

• To: mathgroup at smc.vnet.net
• Subject: [mg29618] convert an expression to an infinite series
• From: "Toshiyuki \(Toshi\) Meshii" <meshii at mech.fukui-u.ac.jp>
• Date: Thu, 28 Jun 2001 05:28:07 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hello,

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?

-Toshi

```

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