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Trying to get closed form solution to simple recurrence.

• To: mathgroup at smc.vnet.net
• Subject: [mg100017] Trying to get closed form solution to simple recurrence.
• From: negatron <lokieffect at gmail.com>
• Date: Fri, 22 May 2009 01:42:02 -0400 (EDT)

Product[(100 - n)/100, {n, 1, x}]

((100!/(100 - (x + 1))!)*(1/100)^(x + 1))

So the two above are equivalent (perhaps the second can do with less
brackets).

What I'm trying to figure out is how to get Mathematica to solve such
a problem. That is, input the first expression and get the second.

I'm aware of the RSolve function and I've used it in the past, but I
can't seem to figure out a way how to express this properly, or more
likely it doesn't look like such a problem can be solved by this
particular function.

Is such a thing solvable by any function in Mathematica?

• Follow-Ups:
  • Re: Trying to get closed form solution to simple recurrence.
    • From: Daniel Lichtblau <danl@wolfram.com>