function [sums,approxerror,realerror] = student_solution(x,numberofsums)


n = 2;
sums = zeros(numberofsums,1);
approxerror = zeros(numberofsums,1);
realerror = zeros(numberofsums,1);
sums(1) = x - x^3/factorial(3);
approxerror(1) = abs((sums(1) - x)/ sums(1));
realerror(1) = abs((sin(x)-sums(1))./sin(x));

if numberofsums ~= 1

    for n = 2:(numberofsums )

        v1 = x^(2*n + 1)/ factorial(2*n + 1) *(-1)^n;

        sums(n) = sums(n-1) + v1 ;


        approxerror(n) = abs((sums(n) - sums(n - 1)) / sums(n));

        realerror(n) = abs((sin(x) - sums(n))./sin(x));

    end
end