Taylor series of log(x) with a = 1.

How to Write a Matlab function that sums up a specified number of terms from the Taylor series of log(x) with a = 1.

%I need my own sript.
%I tried this: 
function s = etaylor_log(x, n)
 syms x
s = taylor(log(x), 'ExpansionPoint', 1, 'Order', n+1)
 end
% It does not give values. 
% The second : 
function s = etaylor_log(x, n)
for i=1:n;
 
    y(i) = (x-1).^(i-1)*(x-1).^i/i;
 
end
s=sum(y);
% it does not show for n=0.

[James Tursa]

Are you allowed to use the MATLAB taylor( ) function or do you have to write this from scratch?

[Ibrahima Diallo]

%I need my own sript.
%I tried this: 
function s = etaylor_log(x, n)
 syms x
s = taylor(log(x), 'ExpansionPoint', 1, 'Order', n+1)
 end
% It does not give values. 
% The second : 
function s = etaylor_log(x, n)
for i=1:n;
 
    y(i) = (x-1).^(i-1)*(x-1).^i/i;
 
end
s=sum(y);
% it does not show for n=0.

[Walter Roberson]

When n is 0 then for i=1:n will not execute at all, so you will not create the variable y

Answer 1

[Kritika Bansal]

Hi,

Taking the analogy from the expression returned by the following command:

taylor(log(x), x, 'ExpansionPoint', 1, 'Order', n); 

You can design your script as follows:

function s = etaylor_log(x, n)
    if n==0
        error("The value of order can only be a positive integer i.e. n>0");
    end 
    if n == 1
        s = 0;
        return;
    end
    for i=1:n-1
        y(i) = ((x-1).^(i)*(-1).^(i-1))/i;
    end
    s=sum(y);
end

Hope this helps!