restart;
An:=1/(4*n+1)+1/(4*n+3)-1/(2*n+2);
Bn:=1/2^(4*n)+1/2^(4*n+2)-1/2^(2*n+1);
S5:=sum(An,n=0..5);
evalf(S5-3/2*ln(2));
S10:=sum(An,n=0..10);
evalf(S10-3/2*ln(2));
S20:=sum(An,n=0..20);
evalf(S20-3/2*ln(2));
S200:=sum(An,n=0..200);
evalf(S200-3/2*ln(2));
S2000:=sum(An,n=0..2000):
evalf(S2000-3/2*ln(2));
an:=(-1)^(n+1)*1/n;
s10:=sum(an,n=1..10);
evalf(s10-ln(2));
s100:=sum(an,n=1..100);
evalf(s100-ln(2));
s2000:=sum(an,n=1..2000):
evalf(s2000-ln(2));
evalf(2/3);
T5:=sum(Bn,n=0..5);
evalf(T5);
T100:=sum(Bn,n=0..100);
evalf(T100);
Bn;
bn:=(-1)^n/2^n;
t5:=sum(bn,n=0..5);
evalf(t5);
t10:=sum(bn,n=0..10);
evalf(t10);
t1000:=sum(bn,n=0..1000):
evalf(t1000);
f:=x^2-2;
plot(f,x=0..Pi);
df:=diff(f,x);
phi:=unapply(x-f/df,x);
x1:=3/2;
x2:=phi(x1);
x3:=phi(x2);
x4:=phi(x3);
evalf(sqrt(2));
evalf(x4);
Digits:=40;
f:=exp(-x)-ln(x);
plot(f,x=0..2);
x1:=1.5;
df:=diff(f,x);
phi:=unapply(x-f/df,x);
x2:=phi(x1);
x3:=phi(x2);
x4:=phi(x3);
x5:=phi(x4);
x6:=phi(x5);
x7:=phi(x6);
x8:=phi(x7);