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restart;
S:=n->Sum(1/k,k=1..n);
T:=n->Sum(1/k^2,k=1..n);
value(S(10));
value(T(10));
p:=[seq([n,value(S(n))],n=1..30)];
with(plots);
P1:=plot(p,color=magenta);
P2:=plot(log(n+1),n=1..30);
display(P1,P2);
U:=n->Sum(1/(k+1),k=1..n);
q:=[seq([n,value(U(n))],n=1..30)];
P3:=plot(q,color=black);
display(P1,P2,P3);
r:=[seq([n,value(T(n))],n=1..100)]:
P4:=plot(r,color=blue);
P5:=plot(Pi^2/6,n=1..100);
display(P4,P5);
limit(T(n),n=infinity);

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