//ramanujan's method //example 2.23 //page 47 clc;clear;close; deff('y=f(x)','1-(x-x^2/factorial(2)^2+x^3/factorial(3)^2-x^4/factorial(4)^2)'); a1=1,a2=-1/(factorial(2)^2),a3=1/(factorial(3)^2),a4=-1/(factorial(4)^2),a5=-1/(factorial(5)^2),a6=1/(factorial(6)^2); b1=1; b2=a1; b3=a1*b2+a2*b1; b4=a1*b3+a2*b2+a3*b1; b5=a1*b4+a2*b3+a3*b2; printf('\n\n%f',b1/b2); printf('\n%f',b2/b3); printf('\n%f',b3/b4); printf('\n%f',b4/b5); printf('\n it appears as if the roots are converging at around %f',b4/b5);