How i do Taylor series summation method?

Answer 1

[Setsuna Yuuki.]

I hope it helps you!

% Integral 
syms y;
fun = @(y) asin(y);
resInt = integral(fun,0,1);

% Taylor loop with 80 component
syms x;
sumatoria = 0; maxi = 80;
serie = zeros(1,maxi); expo = zeros(1,maxi);
for n = 1:maxi
    k = n-1;
    serie(n) = factorial(2*k)/((4^k)*((factorial(k))^2)*(2*k+1));
    expo(n) = 2*k+1;
    sumatoria = sumatoria + serie(n)*x^(expo(n));
end

func = matlabFunction(sumatoria)
resLoop = integral(func,0,1);

% Using the "taylor" command, with 5 components
sumatoria = taylor(fun,y);
func = matlabFunction(sumatoria)
resTaylor = integral(func,0,1);

result = table(resInt, resLoop, resTaylor);