Accuracy problem in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg49061] Accuracy problem in Mathematica
• From: "aaaa" <aaa at huji.ac.il>
• Date: Wed, 30 Jun 2004 05:34:09 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hello,

I'm having a problem with a calculation in Mathematica which I can't
solve. I have an expression which I know to be (from analytical reasons)
always between 0 and 1. It's a function of a and n ( n being natural and
a rational) and it looks like this:

1/(1-a^2)^n +

Sum[((2*n - k - 1)!/((n - 1)!*(n - k)!*2^(2*n - k)))*(1/(1 + a)^k - 1/(1
- a)^k), {k, 1, n}]

Let's say a=0.5.

Now, when I try to calculate for small n, it's ok. When calculating for
large n's (around 400 and above) I'm starting to get wrong results (the
number not being between 0 and 1). The problem is that the first term
(the first line before the sum) is VERY VERY close to the negative of
the second term (the sum), and it's getting closer as n grows. When
using large n's, Mathematica says they are the same number or even that
the last term is bigger (which means the whole expression becomes
negative) - which is wrong. It's a matter of accuracy, and I'm not sure
how I can fix it.

Can anybody help me?

Itamar

```

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