m = 23;

a = zeros(2^m,1);

%a = zeros(1,2^m);

for k=1:m
    
    n(k) = 2^k;
    
    tic;
    for i=1:2^k
        a(i) = (-1)^(i+1)/(2*i-1);
    end
    t1coeff(k) = toc;
    tic;
    for i=1:2:2^k
        a(i) = 1/(2*i-1);
        a(i+1) = -1/(2*i+1);
    end
    t2coeff(k)=toc;
%     clear b;
%     tic;
%     for i=1:2^k
%         b(i) = (-1)^(i+1)/(2*i-1);
%     end
%     t3coeff(k) = toc;
end

for k=1:m
    
    s(k) = 0;
    
    tic;
    for i=1:2^k
        s(k) = s(k) + a(i);
    end
    t1sum(k) = toc;
    tic;
    s(k) = sum(a(1:2^k));
    t2sum(k) = toc;
end

for k=1:m
    
    s(k) = 0;
    
    tic;
    for i=1:2:2^k
        s(k) = s(k) + 1/(2*i-1) - 1/(2*i+1);
    end
    ttot(k) = toc;
end