Ploting a series and finding lim to infinity

Hello everyone, having compute the following series:

n=1:100;
a(1)=1/3;
a(2)=2/7;

a(n+2)=a(n+1)/(n+1)*a(n);

I want to plot the following ratio: a(n+1) / a(n) with the highest possible n and its limit towards infinity.

Thank you in advance!

[KSSV]

What have you tried?

[Destro Katramis]

Well something embarassing like this:

seq=zeros(1,100);
for n=1:100
    seq(n)=a(n+1)/a(n);
end
plot(seq)

Answer 1

[madhan ravi]

N = 1e2; % an inf number 
a = zeros(1,N);
a(1) = 1/3;
a(2) = 2/7;

for n = 1:N-2
    a(n+2) = a(n+1) / (n+1) * a(n); % not sure whether if it should be ((n+1) * a(n))
end

seq = a(2:end) ./ a(1:end-1);

plot(seq)