f:=(x,n)->sum((-1)^k/(2*k+1)*x^(2*k+1),k=0..n);
evalf(4*f(1,50000));evalf(Pi);
evalf(4*f(1,50000)-Pi);
evalf(4*(f(0.5,13)+f(1/3,13)));evalf(Pi);
evalf(4*(f(0.5,13)+f(1/3,13))-Pi);
4*(f(0.5,13)+f(1/3,13))-Pi;
evalf(4*(f(0.5,12)+f(1/3,12))-Pi);
ode:=diff(y(x),x)*(1+2*x)+y(x)=0;
dsolve({ode,y(0)=1},y(x));
evalf(int(sin(x)/x,x=0..1));evalf(1703/1800);
evalf(int(sin(x)/x,x=0..1)-1703/1800);
evalf(1/35280);
factorial(7)*7;
taylor(1/sqrt(1 + 2*x),x=0);
f:=n->sum(1/factorial(k),k=0..n);
f(8);
evalf(f(8));exp(1);evalf(exp(1));
evalf(f(8)-exp(1));