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From: "Jonathan " <jauni6@hotmail.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Nonlinear functions need to find the accuracy
Date: Fri, 9 Apr 2010 00:46:22 +0000 (UTC)
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X can be any value of my choosing, but for the sake of simplicity, I have chosen x=1.  Mathematically, I know I can break the summation into two parts.  The first part would be the function evaluated from k=1 to N-1.  The second part would be an integration of the function from N to infinity.  To define accuracy better, I want the second part (the integration part) to be equal to 10^-8.  I've taken another crack at it, seperated into three parts.  In my code, I manipulate the function.  Here is my code thus far:

clc
syms z k
%
x=1;
f=(1+z)^(1/2)
g=taylor(f,3);
h=subs(g,x/k^3,z);
i=int(h*k^(-3/2),k);
j=abs(i);
%
k1=(1-z)^(1/2)
l=taylor(k1,3);
m=subs(l,x/k^3,z);
n=int(m*k^(-3/2),k);
o=abs(n);
%
p=k-f;
q=taylor(p,3);
r=subs(q,z,x/k^3);
s=int(r*k^(-3/2),k);
t=abs(s)
%
k=1;
t=0;
while s<(1/10^8);    
    k=k+1;
    s=t+s;
end
disp(s)
disp(k)