> limit(product(2^(k/(2^k)),k=1..n),n=infinity);

> limit(Sum((k/2^k),k=1..n),n=infinity);

> rsolve({f(n+2)=f(n+1)+2*f(n),f(0)=-4,f(1)=-2},f(n));

> rsolve({u(n+2)=u(n+1)+u(n),u(0)=1,u(1)=1},u(n));

> makeproc(rsolve({u(n+2)=u(n+1)+u(n),u(0)=1,u(1)=1},u(n)),n=[1..10]);

> with(student);

> f:=makeproc(rsolve({u(n+2)=u(n+1)+u(n),u(0)=1,u(1)=1},u(n)));

> f(2);

> restart;
with(student);

> f:=makeproc(rsolve({u(n+2)=u(n+1)+u(n),u(0)=1,u(1)=1},u(n)),n);

> f(2);

> restart;
> s:=isolate(sqrt(1+x)=1+(x/(2*sqrt(1+t*x))),t);

> limit(s,x=0);

> restart;
> f(x):=5*sin(x)/x;

> plot(f(x),x=-30..30);

> restart;
> f(x):=(x^2-1)/(x*ln(x));

> y:=x:plot([f(x),y(x)],x=0..infinity);

> limit(f(x)-x,x=infinity);

> restart;
> ti:=solve(x^4-x^2+3,x);

> Sum(ti^3/(ti^4-1),ti=1..4);
> 

> sum(op(i,[ti])^3/(op(i,[ti])^4-1),i=1..4);

> restart;
> f:=x->x^(2*n)-(n^2)*x^(n+1)+2*(n^2-1)*x^n-n^2*x^(n-1)+1;

> simplify(D(f)(x));

> subs(x=0,%);

> i:=0;

> while(sub(x=0,%)=0)
do f:=simplify(D(f)(x));
i:=i+1;
od;
i;

> restart;
> p:=x->x^7+27*x^4-x^3-27;

> convert(1/p(x),parfrac,x);

> p:=x->x^4+x^2+1;

> convert(1/p(x),parfrac,x);

> f:=x->1/(x^2+1);
plot(f(x),x=-1..3);

> taylor(f(x),x=0,10);

> t(x):=convert(taylor(f(x),x=0,10),polynom);

> plot([f(x),t(x)],x=-1..1,y=-2..2);

> plot([f(x),t(x)],x=-5..5,y=-2..2);

> restart;
> divise:=proc(a,b)
local i;
i:=0;
while((i+1)*b <=a) do 
i:=i+1;od;
return i;
end proc:
> divise(5,2);

> modulo:=proc(a,b)
local i;
i:=divise(a,b);
return a-b*i;
end proc:
> modulo(5,6);
divise(5,6);

> restart;
> r:=rand(0..100);
t:=r();
tab:=array(1..t);

> tableau:=proc(tab,t)
local i;
for i from 1 to t
do tab[i]:=r();od;
end proc:
> tableau(tab,t);
Somme:=0;
maax:=0;
for i from 1 to t do
  Somme:=Somme+tab[i];
  tab[i];
  if maax<tab[i] then maax:=tab[i]; fi;
od;
maax;

> Somme_tableau:=proc(tab1,t1,tab2,t2,tab3)
local i,maax,miin;
if t1>t2 then maax:=t1;miin:=t2;
else maax:=t2; miin:=t1; fi;
for i from 1 to min
do tab3[i]:=tab1[i]+tab2[i];od;
return tab3;
end proc:

> t1:=r();
tab1:=array(1..t);
tableau(tab1,t);
t2:=r();
tab2:=array(1..t);
tableau(tab2,t);
if t1>t2 then maax:=t1;miin:=t2;
else maax:=t2; miin:=t1; fi;
tab3:=array(1..maax);
Somme_tableau(tab1,t1,tab2,t2,tab3);

Error, (in Somme_tableau) final value in for loop must be numeric or character

> restart;
> r:=rand(0..100);
t:=r();
tab:=array(1..t);

> tableau:=proc(tab,t)
local i;
for i from 1 to t
do tab[i]:=r();od;
end proc:
> Trie:=proc(tab,t)
local i,j,lim;
lim:=t;
for i from lim to 2 by -1 do
 for j from 1 to i do
  if tab[j]>tab[j-1] then tab[j-1]:=tab[j]; fi;
 od;
od;
end proc:

> AfficheTab:=proc(tab,t)
local i;
for i from 1 to t do
   tab[i];
od;
end proc:
> t:=r();
t:=5;
tab:=array(1..t);
tableau(tab,t);
for i from 1 to t do
   tab[i];
od;
Trie(tab,t);
for i from 1 to t do
   tab[i];
od;
> 
> 

Error, (in Trie) 1st index, 0, smaller than lower array bound 1

>