The code below sums the series, starting from the biggest and smallest number. In ideal world the result should be the same and should not saturate, here the series “converge”. Takes a while to run.

% This is sum file

% OK?

%Partial Sum

%S1=1+1/2+1/3+...+1/N, N=10 to the power k

%S2=1/N+...+1/3+1/2+1, N=10 th the power k

%Compares the two

x kmax=10;

clear x;

x=[];

format long e;

for k=1:kmax

n=10 k

s1=0;s2=0;

for p=1:n

s1=s1+1/p;

s2=s2+1/(n-p+1);

end

x=[x;n,s1,s2,s1-s2]

end

disp(x);