> k:=n->sum((binomial(-1/2,k)*(-1)^k)/((2*k+1)*2^(2*k+1)),k=0..n);

k := proc (n) options operator, arrow; sum(binomial...

> k(3);

112579/215040

> a3:=evalf(6*k(3));

a3 := 3.141155134

> l:=n->6*k(n);

l := proc (n) options operator, arrow; 6*k(n) end p...

> eval(l(1));

25/8

> evalf(l(1));

3.125000000

> eval(l(2));

2009/640

> evalf(l(2));

3.139062500

> eval(l(3));

112579/35840

> evalf(l(3));

3.141155134

> evalf(l(4));

3.141511172

> eval(l(4));

10808809/3440640

> b:=evalf(l(10));

b := 3.141592647

> c:=evalf(l(100));

c := 3.141592654

> d:=evalf(l(20));

d := 3.141592654

> evalf(Pi-b);

.7e-8

> evalf(Pi-c);

0.

> evalf(Pi-d);

0.

>