MATLAB: les progs

voilaaa ! TP1
exo 1: Limite
q1,a:

%% 1. Limite
%% question 1, première suite
s=0;
for n=0:100000
s=s+(((-1)^n)/(n+1));
end
disp(s)

Excellent !!!!!!!

q1b:

%% 1. Limite
%% question 1,b
s=0;
for n=1:1000000
s=s+(1/(n^2));
end
disp(s)

Magnifique !! (et oui fo inové ^^)

%% 1. Limite
%% question 2
u=0;
for n=0:100
u=pi*(((((n/(exp(1)))^n)*sqrt(n))/factorial(n))^2);
end
disp(u)

%% 1. Limite
%% question 3
s=0;
for n=0:50
s=s+((((-1)^n)*(((pi)^((2*n)+1)))/((factorial((2*n)+1))*(2^(2*n+1)))));
end
disp(s)

Oulaaa mais c'est un festivals

%% 1. Limite
%% question 4
s=0;
for n=0:50
s=s+(((factorial(n))^2)*((2^(n+1))/(factorial((2*n)+1))));
end
disp(s)

I q1 a
sum ({n geslant 0 }) ((-1)^n / (n+1))

q1 b
sum (n geslant 1) (1/n^2)

q2
u_{n} = %pi times(({({n} over {e})^{n}*sqrt{n} } over {fact {n} } )^{2})

I
q3
sum ({n geslant 0 })(-1)^n {%pi^(2n+1)} over {fact(2n+1)2^(2n+1)}

I q4
sum ({n geslant 0 })(fact n)^2 {2^(n+1)} over {fact (2n+1)}

II q1
f_{n}:t toward (1+{t} over {n})^n

III

q1
sum ({n geslant 0 }) {n^n sqrt{n} } over {fact n} *z^n

III
q2
sum ({n geslant 0 }) ({n-1} over {n})^(n^2)*z^n

%% 3. Rayon de convergence
%% question 1

Rmax=1;
z=0:0.001:Rmax;
s=0;
for n=0:120;
s=s+((((n.^n)*sqrt(n))/(factorial(n)))*z.^n);
end
semilogy(z,s)
grid on


++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

%% 3. Rayon de convergence
%% question 2

Rmax=100;
z=0:0.01:Rmax;
s=0;
for n=0:500;
s=s+((((n-1)/n).^(n.^2))*z.^n);
end
semilogy(z,s)
grid on