% Script: Nfourth
% rate of convergence of sequence (1+1/n^2)-e^(1/n^2), n>=1
% compared with 1/n^4
%
 close all
 n = linspace(1,100);     % evenly spaced values at integers
 one_over_n2 = n.^-2; one_over_n4 = n.^-4; 
 a_n = -(1+one_over_n2)+exp(one_over_n2);
 loglog(n,one_over_n4,'-',n,a_n,'--')
 legend('n^{-4}','e^{n^{-2}} - 1 - n^{-2}',1)
 title('Rate of Convergence for e^{n^{-2}}-1-n^{-2}')
 xlabel('n')
 ratio = a_n./one_over_n4