Power series example: converges for 4 <= x < 6

> restart:
a:=n->(x-5)^n/n;
N:=6;
for n from 1 to N do
s[n]:=add(a(i),i=1..n);
od;

etc.

> N:=20;
for n from 1 to N do
s[n]:=add(a(i),i=1..n);
od:
ss:=-log(6-x);
plot([seq(s[n],n=1..N),ss],x=3.9..6.1,-2..5,
thickness=[seq(1,n=1..N),2],color=[seq(black,n=1..N),red],numpoints=200);

> plot([seq(s[n],n=1..N),ss],x=3.9..4.3,
thickness=[seq(1,n=1..N),3],color=[seq(black,n=1..N),red],numpoints=200);

> plot([seq(s[n],n=1..N),ss],x=5.9..6.1,
thickness=[seq(1,n=1..N),3],color=[seq(black,n=1..N),red],numpoints=200);

>

>